id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
800,870 | AMR-147-0001 | Open Problems in Pluripotential Theory — Question 1 | [Bedford]
Given $\varphi$ an arbitrary plurisubharmonic function in some domain $\Omega \subset {\mathbb{C}}^n$, what can be said about the set of cluster points
of $(dd^c \varphi_j)^n$, where $\varphi_j$ are bounded plurisubharmonic functions which decrease to $\varphi$ ? | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 1
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,871 | AMR-147-0002 | Open Problems in Pluripotential Theory — Question 2 | [Bedford]
Given $\varphi$ a bounded plurisubharmonic function in some domain $\Omega \subset {\mathbb{C}}^n$, what can be said about the set of cluster points of
$(dd^c \varphi_j)^n$, where $\varphi_j$ are bounded plurisubharmonic functions which converge to $\varphi$ in $L_{loc}^1$ ? | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 2
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,872 | AMR-147-0003 | Open Problems in Pluripotential Theory — Question 3 | When $n=1$, maximal plurisubharmonic function are precisely harmonic ones, in particular they are smooth, but in higher dimension they may be quite irregular: a plurisubharmonic function that only depends on
$n-1$ variables is maximal. When $\varphi \in DMA(\Omega)$ then
$$
\varphi \text{ is maximal } \Longleftrightarr... | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 3
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,873 | AMR-147-0004 | Open Problems in Pluripotential Theory — Question 4 | [Dujardin]
Assume $0 \leq \alpha <1$ and $n=2$.
Assume $\varphi$ is ${\mathcal{C}}^{2,\alpha}$-smooth and maximal. Is the suppport of $dd^c \varphi$ foliated (or laminated)
by holomorphic disc along which $\varphi$ is harmonic ? | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 4
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,874 | AMR-147-0005 | Open Problems in Pluripotential Theory — Question 5 | The (global) domain of definition $DMA(X,\omega)$ of the complex Monge-Amp\`ere operator
$\varphi \mapsto (\omega+dd^c \varphi)^n$ is different than its local counterpart
$DMA_{loc}(X,\omega)$.
The construction of Blocki [Blo04] breaks down here as the total mass of
the Monge-Amp\`ere measures of any approximating sequ... | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 5
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,875 | AMR-147-0006 | Open Problems in Pluripotential Theory — Question 6 | Let $\varphi$ be a plurisubharmonic function in the unit ball ${\mathbb{B}}$ of ${\mathbb{C}}^n$. Assume $\varphi$ has a well-defined
complex Monge-Amp\`ere measure $(dd^c \varphi)^n$, we could for instance
assume that $\varphi$ is locally bounded outside the origin.
[Guedj, Rashkovskii]
Assume that $(dd^c \varphi)^n ... | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 6
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,876 | AMR-147-0007 | Open Problems in Pluripotential Theory — Question 7 | As observed by Demailly in [Dem93], it follows from the Ohsawa-Takegoshi theorem that
the $\varphi_j$'s approximate $\varphi$ in a very accurate manner, hence motivating the following:
[Demailly]
Does one have $(dd^c \varphi_j)^n(0) \longrightarrow (dd^c \varphi)^n(0)$ ? | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 7
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,877 | AMR-147-0008 | Open Problems in Pluripotential Theory — Question 8 | [Coman-Guedj]
Assume $(X,\omega)$ is the complex projective space ${\mathbb{C}}\mathbb{P}^n$ equipped with the Fubini-Study K\"ahler form. Can one find examples of a $\omega$-psh function $G_a \in DMA(X,\omega)$, whose Monge-Amp\`ere measure is concentrated at some point $a \in {\mathbb{C}}\mathbb{P}^n$ and having an i... | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 8
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,878 | AMR-147-0009 | Open Problems in Pluripotential Theory — Question 9 | It has been shown in [BEGZ10, Theorem 1.16] that two cohomologous positive closed currents
$T \sim S$ satisfy
$$
\langle T^n \rangle \leq \langle S^n \rangle
$$
if $T$ is more singular than $S$ and both currents have *small unbounded locus*, i.e. their local potentials are locally bounded outside a closed complete plur... | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 9
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,879 | AMR-147-0010 | Open Problems in Pluripotential Theory — Question 10 | A subtle point is to understand precisely when a function $\varphi \in DMA(X,\omega)$ belongs to
${\mathcal{E}}(X,\omega)$. This has been investigated in [CGZ08] with poor success:
[Coman-Guedj-Zeriahi]
Assume $\varphi \in DMA(X,\omega)$ is such that $MA(\varphi)$ does not charge $(\varphi=-\infty)$.
Does it imply tha... | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 10
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,880 | AMR-147-0011 | Open Problems in Pluripotential Theory — Question 11 | [Phong]
Let $X \stackrel{\pi}{\rightarrow} {\mathbb{C}}\mathbb{P}^2$ be the blow up of the complex projective plane at one point.
This is a DelPezzo surface, hence its first Chern class is positive.
Pick $\omega \in c_1(X)$ a K\"ahler form,
$D$ a smooth anticanonical divisor, and let $\mu_D=\omega \wedge [D] /V$ denote... | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 11
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,881 | AMR-147-0012 | Open Problems in Pluripotential Theory — Question 12 | We now focus on the case of *bounded* and *continuous* plurisubharmonic functions.
Although it is the setting of the original breakthrough of Bedford and Taylor [BT76,BT82],
the range of the complex Monge-Amp\`ere operator acting on bounded/continuous (quasi-)psh functions
is yet not characterized (despite rather sharp... | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 12
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,882 | AMR-147-0013 | Open Problems in Pluripotential Theory — Question 13 | [Ko\l{}odziej]
Assume there is a continuous subsolution to the Dirichlet problem, i.e. there is a continuous
psh function $u$ in $\Omega$ such that $u_{|\partial \Omega} =0$ and
$\mu \leq (dd^c u)^n$ in $\Omega$. Does it imply that there is a continuous solution, i.e.
a continuous psh function $\varphi$ such that $\var... | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 13
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,883 | AMR-147-0014 | Open Problems in Pluripotential Theory — Question 14 | [Ko\l{}odziej]
Let $(X,\omega)$ be a compact K\"ahler manifold. Let $\mu$ be a probability measure which is
locally dominated by the Monge-Amp\`ere measures of bounded plurisubharmonic functions.
Can one find $\varphi \in PSH(X,\omega) \cap L^{\infty}(X)$ such that
$\mu=MA(\varphi)$ ? | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 14
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,884 | AMR-147-0015 | Open Problems in Pluripotential Theory — Question 15 | [DDGHKZ]
Are the following properties equivalent ?
(i) There exists $\varepsilon_{\mu}>0$ such that $\exp(-\varepsilon_\mu PSH(X,\omega) ) \subset L^1(\mu)$.
(ii) There exists $\varphi \in {\mathcal{H}ol}(X,\omega)$ sucht that $\mu=MA(\varphi)$. | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 15
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,885 | AMR-147-0016 | Open Problems in Pluripotential Theory — Question 16 | [Zeriahi]
Let $\mu$ be a probability measure in a bounded pseudoconvex domain $\Omega \subset {\mathbb{C}}^n$.
Assume there is a H\"older continuous subsolution to the Dirichlet problem, i.e. there is a
H\"older continuous psh function $u$ in $\Omega$ such that $u_{|\partial \Omega} =0$ and
$\mu \leq (dd^c u)^n$ in $\O... | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 16
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,886 | AMR-147-0017 | Open Problems in Pluripotential Theory — Question 17 | It is interesting that no PDE proof of the above fact is known.
[Blocki-Ko\l{}odziej]
Find a proof of the above estimate that relies on PDE techniques. | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 17
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,887 | AMR-147-0018 | Open Problems in Pluripotential Theory — Question 18 | If the form $\omega$ is merely semi-positive and big (i.e. $\int_X\omega^n>0$) then solutions to the Monge-Amp\`ere equations with $L^p$- right hand sides are continuous as shown in [EGZ11] by using viscosity techniques (solutions are then unique up to an additive constant). Further regularity is then largely open. In ... | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 18
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,888 | AMR-147-0019 | Open Problems in Pluripotential Theory — Question 19 (Berman) | Let $\mu_S$ denote the normalized $n$-dimensional Hausdorff measure on a smooth totally real manifold $S \subset X$ of maximal real dimension $n$.
It has been shown by Sadullaev in [Sad] that $S$ is non pluripolar, hence $\mu_S$ is the Monge-Amp\`ere measure
$\mu_S=(\omega+dd^c \varphi_S)^n$ of a unique function $\varp... | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 19
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Berman | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,889 | AMR-147-0020 | Open Problems in Pluripotential Theory — Question 20 | Let $\alpha \in H^{1,1}(X,{\mathbb{R}})$ be a big cohomology class, $\mu$ a smooth volume form and let $T$ be the unique finite energy current in $\alpha$ such that
$\langle T \rangle^n=\mu$.
Is $T$ smooth in $Amp(\alpha)$ ? | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 20
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,890 | AMR-147-0021 | Open Problems in Pluripotential Theory — Question 21 (DiNezza-Lu) | Let $(X,\omega)$ be a compact $n$-dimensional K\"ahler manifold.
Assume $\varphi \in {\mathcal{E}}(X,\omega)$ solves the equation $(\omega+dd^c \varphi)^n=f\omega^n$, with $f\in L^1$ being
smooth off a divisor $D\subset X$. Is the function $\varphi$ smooth on $X\setminus D$? | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 21
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: DiNezza-Lu | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,891 | AMR-147-0022 | Open Problems in Pluripotential Theory — Question 22 | [Blocki]
Let $\Omega \subset {\mathbb{C}}^n$ be a bounded hyperconvex domain.
Let $u$ be the unique continuous plurisubharmonic function in
$\Omega$ such that $u_{| \partial \Omega}=0$ and
$$
(dd^c u)^n=f dV,
$$
with $f$ smooth and bounded away from zero $f \geq \varepsilon >0$. Is $u$ automatically smooth ? | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 22
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,892 | AMR-147-0023 | Open Problems in Pluripotential Theory — Question 23 | [Blocki-Dinew]
Let $u$ be a plurisubharmonic function in a smooth strictly pseudoconvex bounded domain
$\Omega \subset {\mathbb{C}}^n$. Assume $u \in {\mathcal{C}}^{1,\alpha}(\Omega),\alpha>1-\frac2n$ and
$$
(dd^c u)^n=f dV,
$$
with $f$ smooth and bounded away from zero $f \geq \varepsilon >0$. Is $u$ automatically smo... | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 23
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,893 | AMR-147-0024 | Open Problems in Pluripotential Theory — Question 24 | [Demailly]
Fix $\Omega \subset {\mathbb{C}}^n$ a smooth strictly pseudoconvex bounded domain, and
$\phi \in {\mathcal{C}}^{1,1}(\partial \Omega)$.
Let $u$ be the unique plurisubharmonic function in $\Omega$, continuous up to the boundary,
such that $u=\phi$ on $\partial \Omega$ and
$$
(dd^c u)^n=0 \; \;
\text{ in } \; ... | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 24
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,894 | AMR-147-0025 | Open Problems in Pluripotential Theory — Question 25 | Bedford and Fornaess [BeFo] have shown that $u$ need not belong to $\mathcal{C}^2(\bar{\Omega})$ under the assumptions above. Their construction relies on the boundary behavior of the $\mathcal{C}^2$ norm.
Under what minimial assumptions does $u$ belong to $\mathcal{C}^2(\Omega)$ ? | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 25
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,895 | AMR-147-0026 | Open Problems in Pluripotential Theory — Question 26 (Blocki) | It is easy to prove that for a hyperconvex domain $\Omega$ and a fixed pole $w$ one has
$$\lim_{z\rightarrow\partial\Omega}g_{\Omega}(z,w)=0.$$
Is it true that for a bounded hyperconvex domain $g_{\Omega}(z,w)$ converges locally uniformly to zero, as the pole $w$ converges to the boundary of $\Omega$? | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 26
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Blocki | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,896 | AMR-147-0027 | Open Problems in Pluripotential Theory — Question 27 (Blocki) | Let $\Omega$ be smoothly bounded strictly pseudoconvex domain. It is known that $g_{\Omega}\in\mathcal{C}^{1,1}(\Omega\setminus\lbrace w\rbrace)$. Is there an example where $g$ fails to be in $\mathcal{C}^2(\Omega\setminus\lbrace w\rbrace)$? | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 27
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Blocki | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,897 | AMR-147-0028 | Open Problems in Pluripotential Theory — Question 28 (Dinew-Ko\l{}odziej) | Let $(X,\omega)$ be a compact Hermitian manifold of dimension greater or equal to $3$.
Characterize the forms $\omega$ for which $\int_X(\omega+dd^c\varphi)^n=\int_X\omega^n$ for any bounded $\omega$-plurisubharmonic function
$\varphi$. | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 28
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Dinew-Ko\l{}odziej | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,898 | AMR-147-0029 | Open Problems in Pluripotential Theory — Question 29 (Tosatti) | Let $(X,\omega)$ be a compact Hermitian manifold. Define $T(X,\omega)$ by
$$
T(X,\omega)=\inf \left\lbrace\int_X(\omega+dd^c\varphi)^n|\ \varphi\in\mathcal{C}^{\infty}(X)\cap PSH(X,\omega) \right\rbrace.
$$
Is it possible that $T(X,\omega)=0$ for some manifold? | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 29
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Tosatti | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,899 | AMR-147-0030 | Open Problems in Pluripotential Theory — Question 30 (Dinew-Ko\l{}odziej) | Let $(X,\omega)$ be a compact Hermitian manifold. Define $cap(X,\omega)$ by
$$
cap(X,\omega)=\inf \left\lbrace\int_X(\omega+dd^c\varphi)^n|\ \varphi\in PSH(X,\omega),\ 0\leq\varphi\leq 1\right\rbrace.
$$
Relate the quantity $cap(X,\omega)$ to the geometry of $(X,\omega)$. In particular is this quantity computable in te... | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 30
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Dinew-Ko\l{}odziej | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,900 | AMR-147-0031 | Open Problems in Pluripotential Theory — Question 31 (Tosatti-Weinkove) | Let $z_1,\cdots,z_k$ be a collection of points on a Hermitian manifold $X$ and let $\tau_1,\cdots,\tau_k$ be a collection of positive numbers satisfying $\sum_{j=1}^k\tau_j^n<\int_X\omega^n$. Construct an $\omega$-plurisubharmonic function, so that $\phi(z)\leq \tau_j \log(||z-z_j||)+O(1)$ near $z_j$. | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 31
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Tosatti-Weinkove | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,901 | AMR-147-0032 | Open Problems in Pluripotential Theory — Question 32 | When $n=\dim_{\mathbb{C}} \leq 2$,
it follows from the work of Blel-Mimouni [BM05], the second author [G05b] and
Favre-Jonsson [FJ05] that $\varphi$ can be further decomposed as follows:
for any $\varepsilon>0$, there exists $\pi_\varepsilon:X_\varepsilon \rightarrow X$ a finite composition of blow-ups
such that
$$
\pi... | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 32
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,902 | AMR-147-0033 | Open Problems in Pluripotential Theory — Question 33 (ACHKZ) | While giving the optimal exponential integrability the result is still not sharp because of the polynomial term in front.
Is it true that (for a different constant $c_n$)
$$
\mathrm{Vol}(\lbrace\varphi<-s\rbrace)\leq c_n\delta_{\Omega}^{2n}exp(-2ns\mu^{-1})?
$$ | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 33
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: ACHKZ | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,903 | AMR-147-0034 | Open Problems in Pluripotential Theory — Question 34 | [Berman-Boucksom-Eyssidieux-Guedj-Zeriahi]
Assume $\varphi \in {\mathcal{E}}(X,\omega)$ is a $\omega$-psh function with finite energy.
Is it true that $\varphi$ has zero Lelong number at all points ? | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 34
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,904 | AMR-147-0035 | Open Problems in Pluripotential Theory — Question 35 | Let $(X,\omega)$ be a compact K\"ahler manifold and $Y \subset X$ a complex submanifold.
It is natural to wonder whether all $\omega$-plurisubharmonic functions on $Y$ are induced by global $\omega$-plurisubharmonic functions:
[Coman-Guedj-Zeriahi]
Is it true that
$$
PSH \left(Y,\omega_{|Y} \right)=PSH(X,\omega)_{|Y} ... | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 35
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,905 | AMR-147-0036 | Open Problems in Pluripotential Theory — Question 36 | [P\u aun]
Can one find $h=e^{-\varphi}$ a hermitian metric of ${\mathcal{L}}$ on ${\mathcal{X}}$ which is a semi-positive extension of $\varphi_0$, i.e.
such that $dd^c \varphi \geq 0$ and $\varphi_{|X_0}=\varphi_0$ ? | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 36
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,906 | AMR-147-0037 | Open Problems in Pluripotential Theory — Question 37 | The point in the example above is that there is no differential test from above for $\varphi$ along the line
$(w=0)$. A simpler example in any dimension is provided by $\varphi(z)=||z||$: there is no differential test from above at the origin; the function is strictly plurisubharmonic in the viscosity sense, but not in... | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 37
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,907 | AMR-147-0038 | Open Problems in Pluripotential Theory — Question 38 | [Eyssidieux-Guedj-Zeriahi]
Let $v$ be a continuous viscosity supersolution of the equation
$$
-(dd^c V)^n+fdV=0.
$$
Is $P(v)$ a pluripotential supersolution of the same equation ? | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 38
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,908 | AMR-147-0039 | Open Problems in Pluripotential Theory — Question 39 | [Eyssidieux-Guedj-Zeriahi]
Let $\omega$ be a smooth semi-positive and big form on a compact K\"ahler manifold $X$.
Is any function $\varphi \in PSH(X,\omega)$ the decreasing limit of smooth $\omega$-psh functions ? | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 39
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,909 | AMR-147-0040 | Open Problems in Pluripotential Theory — Question 41 | When $S_0$ has some non-zero Lelong numbers, DiNezza and Lu construct a maximal family of positive currents
$(\omega_t)_{0<t<T_{max}}$ which are honest K\"ahler forms on a time-increasing family of Zariski open subsets $\Omega_t$ where they satisfy the K\"ahler-Ricci flow equation.
By analogy with Demailly regularizati... | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 41
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,910 | AMR-147-0041 | Open Problems in Pluripotential Theory — Question 42 | Do actually deals with more general flows which contain, as a particular case, the local version of the K\"ahler-Ricci flow. These flows can thus be run from a bounded plurisubharmonic initial data.
The following question is natural, in view of the corresponding global results from [GZ13,DiNL14b]:
[Guedj]
Can one run ... | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 42
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,911 | AMR-147-0042 | Open Problems in Pluripotential Theory — Question 43 | [Eyssidieux-Guedj-Zeriahi]
Assume $u$ (resp. $v$) is a viscosity subsolution (resp. supersolution) to the above degenerate complex
Monge-Amp\`ere flow such that
$u \leq v$ on the parabolic boundary $\{0\} \times X$.
Is it true that that $u \leq v$ on $[0,T] \times X$ ? | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 43
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,912 | AMR-147-0043 | Open Problems in Pluripotential Theory — Question 44 (Dinh) | Lelong numbers are well-defined not only for positive *closed* currents- in particular it is enough to assume that the current is positive and *harmonic* i.e. $dd^c T=0$. The next question deals with Siu- type problem for harmonic currents:
Let $X$ be a compact K\"ahler manifold and $T$ be a positive harmonic current ... | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 44
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Dinh | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,913 | AMR-147-0044 | Open Problems in Pluripotential Theory — Question 45 (Bloom-Leveberg) | The supremum is achieved by the relative extremal function
$$h_K(z)=\limsup_{\zeta\rightarrow z}sup\lbrace u(\zeta)|\ u\in {\mathrm{PSH}}(\mathbb{B}^n),\ u\leq 1,\ u|_K\leq 0\rbrace.$$
The set $K$ is called *regular* if the relative extremal function is continuous.
Given any subset $K$ of positive capacity and $\vare... | Source list: Dinew, Guedj, Zeriahi - Open Problems in Pluripotential Theory (2015)
Source item: Question 45
Source URL: https://arxiv.org/abs/1511.00705
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Bloom-Leveberg | 3 | open | Dinew, Guedj, Zeriahi | 2,015 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,914 | AMR-148-0001 | AGNES Open Problems in Algebraic Geometry — Q1 | Does $\pi_*[\overline{M}_g(X,\beta)]^{\operatorname{vir}}\in H^*(\overline{M}_g)$
lie in the tautological ring in cohomology?
**Q2**.
When does $\pi_*[\overline{M}_g(X,\beta)]^{\operatorname{vir}}\in A^*(\overline{M}_g)$
lie in the tautological ring in Chow?
I would guess the answer to $**Q1**$ is yes. If $X$ is
a cu... | Source list: Pandharipande - Open Problems in Enumerative Algebraic Geometry (AGNES) (2010)
Source item: Q1 (#1)
Source URL: https://arxiv.org/abs/1004.3259
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Pandharipande | 2,010 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,915 | AMR-148-0002 | AGNES Open Problems in Algebraic Geometry — Q3 | Prove the Virasoro constraints in case $X$ is an Enriques surface.
A study of the Gromov-Witten theory of the Enriques surface,
closely related to modular forms, has been started in
[mp2]. The Enriques surfaces
is perhaps the most basic variety where new techniques are
required to establish the Virasoro constraints. | Source list: Pandharipande - Open Problems in Enumerative Algebraic Geometry (AGNES) (2010)
Source item: Q3 (#2)
Source URL: https://arxiv.org/abs/1004.3259
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Pandharipande | 2,010 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,916 | AMR-148-0003 | AGNES Open Problems in Algebraic Geometry — Q4 | Prove the GW/DT correspondence for $3$-folds.
The toric cases of **Q4** are known [moop]. Algebraic cobordism
results [levp] suggest the possibility of
reducing to the toric case using degeneration methods. | Source list: Pandharipande - Open Problems in Enumerative Algebraic Geometry (AGNES) (2010)
Source item: Q4 (#3)
Source URL: https://arxiv.org/abs/1004.3259
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Pandharipande | 2,010 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,917 | AMR-148-0004 | AGNES Open Problems in Algebraic Geometry — Q5 | Donaldson--Thomas invariants are defined only in dimension $3$
because a virtual fundamental class for the moduli space of sheaves
is required.
Deformations are given by $\operatorname{Ext}^1(E,E)$, obstructions by $\operatorname{Ext}^2(E,E)$,
and to define the virtual fundamental class we need (roughly) the
vanishing
... | Source list: Pandharipande - Open Problems in Enumerative Algebraic Geometry (AGNES) (2010)
Source item: Q5 (#4)
Source URL: https://arxiv.org/abs/1004.3259
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Pandharipande | 2,010 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,918 | AMR-148-0005 | AGNES Open Problems in Algebraic Geometry — Q6 | What is the analogue of the tautological ring for $M^{K3}_{2n}$?
A natural guess for **Q6** is the subring generated by the
classes of the
Noether--Lefschetz loci. The Noether-Lefschetz loci parameterize
$K3$ surfaces with higher rank Picard lattices. | Source list: Pandharipande - Open Problems in Enumerative Algebraic Geometry (AGNES) (2010)
Source item: Q6 (#5)
Source URL: https://arxiv.org/abs/1004.3259
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Pandharipande | 2,010 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,919 | AMR-148-0006 | AGNES Open Problems in Algebraic Geometry — Q7 | Do the Noether-Lefschetz divisors span
$\text{Pic}(M^{K3}_{2n}) \otimes_{\mathbb{Z}}{\mathbb{Q}}$?
Let $X$ be a compact
Calabi-Yau 3-fold expressed as $K3$-fibration over $\mathbb{P}^1$,
$$\pi:X\rightarrow \mathbb{P}^1\ .$$
Given an ample line bundle $L$ on $X$, the family $\pi$
determines a morphism of the base $\mat... | Source list: Pandharipande - Open Problems in Enumerative Algebraic Geometry (AGNES) (2010)
Source item: Q7 (#6)
Source URL: https://arxiv.org/abs/1004.3259
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Pandharipande | 2,010 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,920 | AMR-148-0007 | AGNES Open Problems in Algebraic Geometry — Q8 | Prove the Katz-Klemm-Vafa conjecture for in all genera and
in all classes on $K3$ surfaces.
A solution to **Q8** would provide a large class
of exact formulas for higher genus Gromov-Witten invariants of
compact Calabi-Yau 3-folds. Unlike the local toric cases,
mathematical results for higher genus Gromov-Witten invar... | Source list: Pandharipande - Open Problems in Enumerative Algebraic Geometry (AGNES) (2010)
Source item: Q8 (#7)
Source URL: https://arxiv.org/abs/1004.3259
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Pandharipande | 2,010 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,921 | AMR-149-0001 | Open Problems and Questions about Geodesics — Conjecture 1 (Long, Bangert, Problem 15 from [Alvarez2006]) | V. Bangert and Y. Long in [Ban-Lon2010] and [Long2006] proved that there are always at least 2 distinct prime closed geodesics for every irreversible
Finsler metric on $S^2$.
*Every irreversible Finsler metric on $S^2$ has either
exactly $2$ or infinitely many distinct prime closed geodesics.* | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Conjecture 1
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Long, Bangert, Problem 15 from [Alvarez2006] | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,922 | AMR-149-0002 | Open Problems and Questions about Geodesics — Conjecture 2 (Long) | There exist results supporting this conjecture. In particular,
H. Hofer, K. Wysocki and E. Zehnder in [Ho-Wy-Ze2003] studied Reeb orbits on contact $S^3$.
Their result can be projected down to $S^2$, and implies that the total number of distinct prime closed geodesics for a bumpy Finsler metric on $S^2$ is either 2
or ... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Conjecture 2
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Long | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,923 | AMR-149-0003 | Open Problems and Questions about Geodesics — Conjecture 3 (Long) | \begin{con}[Long] *The existence of one hyperbolic prime closed geodesic on a Finsler
$S^2$ implies the existence of infinitely
many distinct prime closed geodesics.* \end{con}
*Every Finsler $S^2$ has at least one elliptic prime closed geodesic.* | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Conjecture 3
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Long | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,924 | AMR-149-0004 | Open Problems and Questions about Geodesics — Question 4 | [Bangert]
*Does every complete Riemannian manifold with finite volume have at least one closed geodesic?* | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 4
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,925 | AMR-149-0005 | Open Problems and Questions about Geodesics — Question 5 (Bangert) | Questions of this nature are also interesting in the realm of Finsler geometry. One would expect the results for reversible Finsler metrics to be very similar to those for Riemannian metrics. For irreversible Finsler metrics, Katok's example shows that there are compact Finsler manifolds with only finitely many closed ... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 5
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Bangert | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,926 | AMR-149-0006 | Open Problems and Questions about Geodesics — Question 6 (Paternain) | It is known that the trajectory of a charged particle in the presence of magnetic forces (=``magnetic geodesic'') is described by a Hamiltonian system with the ``kinetic" Hamiltonian of the form $\sum_{i,j} p_ip_jg^{ij}$ on $T^*M$ with the symplectic form $dp\wedge dx +\pi^* \omega$, where $\omega $ is a closed (but no... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 6
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Paternain | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,927 | AMR-149-0007 | Open Problems and Questions about Geodesics — Question 7 | Recent interest in Kropina metrics is due to their relations to the so-called chains in CR geometry, see [CMMM2019].
*Does every Kropina metric on a closed manifold have a closed geodesic?* | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 7
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,928 | AMR-149-0008 | Open Problems and Questions about Geodesics — Question 8 (Paternain) | Let $p, q$ be points in a Riemannian manifold. The space $\Omega_T(p,q)$ of paths from $p$ to $q$ with length $\leq T$ has the homotopy type of a finite complex (see e.g.\ [Milnor1963]),
and hence the sum of its Betti numbers is finite for each $T$. The same is true for the space $\Lambda_TM$ of loops with length at mo... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 8
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Paternain | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,929 | AMR-149-0009 | Open Problems and Questions about Geodesics — Question 9 (Gromov) | It was shown by Gromov in [Gromov2001] that
if $M$ is simply connected
there is a constant $C$ such that the
sum of the Betti numbers of $\Lambda_{CN}$ is at least
$
\sum_{i=0}^N b_{i}(\Lambda)$.
*Does the number of closed geodesics with length $\leq T$ grow exponentially as $T \to \infty$ if the Betti numbers of the ... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 9
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Gromov | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,930 | AMR-149-0010 | Open Problems and Questions about Geodesics — Question 10 (Hingston) | Let $M$ be a compact manifold with a Riemannian (or Finsler) metric $g$. \
Let $G$ be a finitely generated
abelian group. \ Given a non-trivial homology class
$X \in H_{\ast}(\Lambda M;G)$, the critical (minimax) level of $X$ is
\begin{align*}
cr X & =\inf\{a:X\in\text{Image }H_{\ast}(\Lambda_a M;G)\}\\
& =\underset{x\... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 10
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Hingston | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,931 | AMR-149-0011 | Open Problems and Questions about Geodesics — Conjecture 11 (Hingston) | \begin{align*}
\alpha_{g,G} & =a\text{ if }G=\mathbb{Q}\\
\alpha_{g,G} & =b\text{ if }G = \mathbb{Z}_{3}\\
\alpha_{g,G} & =c\text{ if }G = \mathbb{Z}_{7}\\
\alpha_{g,G} & =a\text{ if }G= \mathbb{Z}_{p},p\neq3,7.
\end{align*} | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Conjecture 11
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Hingston | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,932 | AMR-149-0012 | Open Problems and Questions about Geodesics — Conjecture 12 (Klingenberg) | The class of compact manifolds that support metrics with variable negative curvature is much larger than the class that support hyperbolic metrics (of constant negative curvature). The earliest examples of manifolds that support variable but not constant negative curvature were given by Mostow-Siu [Mos-Siu1980] and Gro... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Conjecture 12
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Klingenberg | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,933 | AMR-149-0013 | Open Problems and Questions about Geodesics — Question 13 | Several examples of manifolds that admit metrics of non-positive curvature but cannot support a metric of negative curvature (or with Anosov geodesic flow) can be found in the introduction to [Ba-Br-Eb1985]. These examples have a copy of ${\mathbb{Z}} \times {\mathbb{Z}}$ in their fundamental group. The simplest of the... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 13
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,934 | AMR-149-0014 | Open Problems and Questions about Geodesics — Question 14 | Again it is not difficult to use the uniformization theorem to show that the answer is affirmative in dimension 2.
But the problem is still open even in dimension 3. See [Cro-Sch1986], [Lebedeva2002] and [Iva-Kap2014] for results of the nature that the fundamental groups of manifolds with no conjugate points share prop... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 14
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,935 | AMR-149-0015 | Open Problems and Questions about Geodesics — Conjecture 15 ([Bur-Kat1985]) | Suppose $(M, g)$ is a closed Riemannian manifold. The marked length spectrum of $M$ is the
function
that assigns to each free homotopy class of loops the
infimum of the length of loops in the class (i.e. the length of the shortest closed geodesic lying in this class).
*Two metrics with negative curvature on a compact ... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Conjecture 15
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: [Bur-Kat1985] | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,936 | AMR-149-0016 | Open Problems and Questions about Geodesics — Question 16 (Benjamin Schmidt) | One can ask a similar question for non-manifolds.
Consider a 2-dimensional (metrical) simplicial complex such that every simplex is hyperbolic with geodesic edges and such that $CAT(-1)$ condition holds on every vertex. Assume in addition that every edge is contained in at least two simplices.
*Does the marked length ... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 16
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Benjamin Schmidt | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,937 | AMR-149-0017 | Open Problems and Questions about Geodesics — Question 17 (Boundary rigidity problem) | The questions above are closely related to the boundary rigidity problem, which we now recall.
Given a compact manifold $M$ with smooth boundary $N$, a
Riemannian metric $g$ on $M$ induces a non-negative real valued function $d$
on
$N \times N$ where $d(p, q)$ is the distance in $(M, g)$ between $p$ and $q$.
We call $(... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 17
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Boundary rigidity problem | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,938 | AMR-149-0018 | Open Problems and Questions about Geodesics — Conjecture 18 | Two Riemannian manifolds $(M_1,g_1)$ and $(M_2,g_2)$ have $C^k$-conjugate geodesic flows if there is an invertible map $h: S^M_1 \to S^M_2$ such that $h$ and $h^{-1}$ are $C^k$ and
$h \circ \phi^1_t = \phi^2_t \circ h$ for all $t$. Here $\phi^i_t$ is the geodesic flow for the metric $g_i$. A long standing conjecture is... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Conjecture 18
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,939 | AMR-149-0019 | Open Problems and Questions about Geodesics — Conjecture 19 ([Katok1982]) | Katok [Katok1982] showed that if $g$ is an arbitrary metric and $g_0$ a metric of constant negative curvature on a surface of genus $\geq 2$ such that $\text{area}(g) = \text{area}(g_0)$, then
$$
h_{Liou}(g) \leq h_{Liou}(g_0) =h_{top}(g_0) \leq h_{top}(g)
$$
and both inequalities are strict unless $g$ also has constan... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Conjecture 19
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: [Katok1982] | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,940 | AMR-149-0020 | Open Problems and Questions about Geodesics — Question 20 | An extensive list of results about the regularity of the Anosov splitting for the geodesic flow in negative curvature (and for other Anosov systems) can be found in the introduction to [Hasselblatt1994]. In dimension two, or if the curvature is $1/4$-pinched, the splitting is always at least $C^1$. In higher dimensions... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 20
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,941 | AMR-149-0021 | Open Problems and Questions about Geodesics — Question 21 | Is there a metric of negative curvature for which the ratio of largest positive Lyapunov exponent to smallest positive Lyapunov exponent is greater than $2$ for typical geodesics (not just exceptional closed geodesics)? | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 21
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,942 | AMR-149-0022 | Open Problems and Questions about Geodesics — Conjecture 22 | Let $(M, g)$ be a closed Riemannian manifold with negative sectional curvatures. It is known [Margulis2004] that the number $N(T)$ of closed geodesics of length $\le T$ grows
asymptotically as ${e^{hT}}/{hT}$.
{\it $N(T)= (1+ O(e^{-\varepsilon T})) \displaystyle \int_2^{e^{hT}} \frac{du}{\log u} $. } | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Conjecture 22
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,943 | AMR-149-0023 | Open Problems and Questions about Geodesics — Question 23 (Miller [Miller2001], Reid) | *Are there infinitely many simple closed
geodesics in every hyperbolic complete three-manifold of finite volume?* | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 23
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Miller [Miller2001], Reid | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,944 | AMR-149-0024 | Open Problems and Questions about Geodesics — Question 24 | *Is the geodesic flow of a metric of
non-positive curvature on a closed
surface of genus $\ge 2$ ergodic with respect to the Liouville measure? * | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 24
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,945 | AMR-149-0025 | Open Problems and Questions about Geodesics — Question 25 | \ Consider a closed surface of genus $\ge 2$.
[Burns] *Is there a $C^\infty$ (or at least $C^k, \ k\ge 3)$ metric
for which there exists a non-closed geodesic along which the Gaussian curvature is everywhere zero?* | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 25
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,946 | AMR-149-0026 | Open Problems and Questions about Geodesics — Question 26 | [Knieper]
*Consider a closed surface of genus $\geq 2$ with a metric of non-positive curvature. Let $Z(L)$ be the number of free homotopy classes containing
closed geodesics with length $\leq L$ along which the curvature is everywhere zero.
Is there a quadratic upper bound for $Z(L)$, i.e.\ is there a constant $C \geq ... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 26
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,947 | AMR-149-0027 | Open Problems and Questions about Geodesics — Question 27 | Let $\alpha$ and $\beta$ be two geodesics in a complete simply connected Riemannian manifold without conjugate points.
*Suppose $\alpha(0)=\beta(0)$. Does $dist(\alpha(t), \beta(t)) \to \infty$ as $t\to \infty$?* | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 27
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,948 | AMR-149-0028 | Open Problems and Questions about Geodesics — Question 28 | The answer is positive in dimension 2 [Green1954]. The question is open in higher dimensions; the proof in [Green1956] is incorrect. The answer to the corresponding question about Finsler metrics is negative. The
Teichm\"uller metric on Teichm\"uller space has no conjugate points, but Masur showed that there exist two ... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 28
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,949 | AMR-149-0029 | Open Problems and Questions about Geodesics — Question 29 ([Bur-Kni1991]) | The simplest question of this type asks if a Riemannian plane satisfying Euclid's 5th postulate must be flat.
Consider the plane $\mathbb{R}^2$ with a complete Riemannian metric. Assume that for every geodesic and for every point not on the geodesic there exists precisely one non-trivial geodesic that passes through th... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 29
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: [Bur-Kni1991] | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,950 | AMR-149-0030 | Open Problems and Questions about Geodesics — Conjecture 30 (Spatzier) | *Let $(M,g)$ be a closed symmetric space of non-compact type and of higher rank. Then the only metrics on $M$ with no conjugate points are homothetic rescalings of $g$.* | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Conjecture 30
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Spatzier | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,951 | AMR-149-0031 | Open Problems and Questions about Geodesics — Conjecture 31 (Burago-Kleiner) | Consider the product of a closed surface $M^2$ of genus $\ge 2$ with the circle $S$. Let $g$ be a Riemannian metric on $M\times S$ with no conjugate points.
{\it The metric on the $\mathbb{Z}$-cover corresponding to $S^1$ factor is a direct product: $(M\times \mathbb{R}, g)=(M, g_1)\times (\mathbb{R}, dt^2)$. } | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Conjecture 31
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Burago-Kleiner | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,952 | AMR-149-0032 | Open Problems and Questions about Geodesics — Question 32 (Paternain) | *Consider a magnetic flow on a closed surface of genus $\ge 2$ and an energy level such that the topological entropy vanishes. Suppose that the magnetic geodesics on this level do not have conjugate points. Is the system locally symmetric in the sense that the metric has constant curvature and the magnetic form
is a co... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 32
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Paternain | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,953 | AMR-149-0033 | Open Problems and Questions about Geodesics — Question 33 | The general problem is still wide open despite some reports of its solution (p. 87 of [Berger2000] and Section 10.9 of [Berger2003]).
*Is there a Riemannian metric on a closed manifold with everywhere positive sectional curvatures and ergodic geodesic flow?* | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 33
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,954 | AMR-149-0034 | Open Problems and Questions about Geodesics — Question 34 (Benjamin Schmidt) | \begin{align*}
T_b &:=\{ v\in SM\mid \textrm{ any lift of $\gamma_v$ stays in a bounded subset of $\widetilde M$}\}, \\
T_p &:=\{ v\in SM\mid \textrm{ any lift of $\gamma_v$
is unbounded, and approaches infinity properly}\}, \\
T_i &:=TM\setminus (T_b \cup T_p).
\end{align*}
All three sets are measurable and invariant... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 34
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Benjamin Schmidt | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,955 | AMR-149-0035 | Open Problems and Questions about Geodesics — Question 35 | We use $C^k$-topology either locally or on closed manifolds, where we may
assume that the atlas is finite and the gluing functions have all derivatives bounded. Then the convergence in the topology means the following: a sequence $g^{(1)},g^{(2)},\dots$ of metrics converges to a metric $g$ in the topology $C^k$ if in l... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 35
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,956 | AMR-149-0036 | Open Problems and Questions about Geodesics — Question 36 | Assume $M$ is closed.
If $\dim(M)\ge 3$, do the metrics for which the geodesic flow is
transitive (i.e.\ has an orbit whose closure is $SM$) form a dense subset of $\mathcal{G}(M)$? | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 36
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,957 | AMR-149-0037 | Open Problems and Questions about Geodesics — Question 37 | This question is closely related to the famous
Arnold diffusion conjecture.
If $\dim(M)=2$ and $k$ is large enough,
the answer is negative: if we take a metric with integrable geodesic flow such that certain
Liouville tori are irrational, and
any small perturbation of the metric has non-transitive geodesic flow by the ... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 37
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,958 | AMR-149-0038 | Open Problems and Questions about Geodesics — Question 38 | In the previous section we discussed the unit tangent bundle $SM$. In this section we ask similar questions about $M$ itself, and we will not assume that the metrics are generic.
*Is the union of the closed geodesics always dense in the manifold?* | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 38
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,959 | AMR-149-0039 | Open Problems and Questions about Geodesics — Problem 40 | Flag curvature is the Finslerian analogue of sectional curvature. It was shown in [Akbar-Zadeh1988] that: any closed Finsler surface with constant flag curvature zero is locally Minkowskian; any sufficiently smooth closed Finsler surface with constant negative curvature is Riemannian (there are non-Riemannian examples ... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Problem 40
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,960 | AMR-149-0040 | Open Problems and Questions about Geodesics — Problem 41 | Moreover, the Finsler metrics satisfying (i) necessary admit a Killing vector field and are quite well understood. Applying the Zermelo transformation to such metrics (see e.g. [Fou-Mat2018]), one obtains non-Zoll metrics satisfying (ii). Moreover, any such metric (of flag curvature $1$ on $S^2$ and satisfying (ii)) ad... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Problem 41
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,961 | AMR-149-0041 | Open Problems and Questions about Geodesics — Question 42 | *Does Frankel's Theorem remain true for Finsler manifolds? More precisely, must two closed
totally geodesic submanifolds of a closed Finsler manifold
with positive flag curvature intersect if the sum of their dimensions is at least the dimension of the ambient manifold? * | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 42
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,962 | AMR-149-0042 | Open Problems and Questions about Geodesics — Question 43 | *Let $(M^3, F)$ be a closed 3-dimensional reversible Finsler manifold of positive flag curvature and $N$ be a closed totally geodesic 2-dimensional submanifold. Is it true that each closed geodesic intersects this submanifold or lies on it?
* | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 43
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,963 | AMR-149-0043 | Open Problems and Questions about Geodesics — Problem 44 (Benjamin Schmidt) | We consider a
Riemannian metric on an oriented closed surface $M$ of genus $\ge 1$. Let $\Gamma$ be a non-trivial
free homotopy class and $p$ a point in $M$. A theorem of Gaidukov [Gaidukov1966] says that
there exist a closed geodesic $\gamma:\mathbb{R}\to M$ in $\Gamma$ and a ray $\beta:[0,\infty)\to M$
with $\beta(0)... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Problem 44
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Benjamin Schmidt | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,964 | AMR-149-0044 | Open Problems and Questions about Geodesics — Question 45 (Babenko) | *Does there exist, in the space of metrics with conical singularities, a (continuous or smooth) family of
metrics $g_t$ such that $g_0$ is the round metric of the sphere, $g_1$ is the metric from the example above, and
$\sigma(g_t)$ is a decreasing function of $t$.* | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 45
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Babenko | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,965 | AMR-149-0045 | Open Problems and Questions about Geodesics — Question 46 (Babenko) | { \it Does every Riemannian metric on $S^2$ with area $4\pi$ that is close enough to the round metric have a closed geodesic with length $\leq 2\pi$? In other words, is it true that $\sigma \ge 1/\pi$ for metrics close to the round metric? } | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 46
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Babenko | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,966 | AMR-149-0046 | Open Problems and Questions about Geodesics — Question 47 (Guth) | For the diastole defined by (a), Balacheff and Sabourau showed in [Bal-Sab2010] that there is a constant $C$ such that
$$
\textrm{dias}(M,g) \leq C\sqrt{\textrm{genus}(M)}\sqrt{\textrm{area}(M, g)};
$$
the dependence of this inequality on the genus is again optimal.
*Is there a constant $C$ such that the invariant def... | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 47
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Guth | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,967 | AMR-149-0047 | Open Problems and Questions about Geodesics — Question 48 (Question 4.11 of [Gromov2001]) | { \it Does a Riemannian metric on a real projective space with the same volume as the canonical metric have a closed geodesic with length $\leq \pi$?} | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 48
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Question 4.11 of [Gromov2001] | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,968 | AMR-149-0048 | Open Problems and Questions about Geodesics — Question 49 (\'Alvarez Paiva) | { \it Can there be Riemannian metrics on $S^3$ or $S^2 \times S^1$ with unit volume all of whose closed geodesics are long? More specifically, does every metric on these spaces have a closed geodesic with length $\leq 10^{24}$ if the volume is $1$?} | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 49
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: \'Alvarez Paiva | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,969 | AMR-149-0049 | Open Problems and Questions about Geodesics — Question 50 | *Let $M$ be a closed manifold not covered by a sphere. Let $g$ be a metric on $M$ for which all geodesics are closed. Is $(M,g)$ a CROSS (=compact
rank one symmetric) manifold (with the standard metric)?* | Source list: Burns, Matveev - Open Problems and Questions about Geodesics (2019)
Source item: Question 50
Source URL: https://arxiv.org/abs/1308.5417
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Burns, Matveev | 2,019 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.