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2fca478 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | import OAI.Geometry.ProjectionBodies.AffineCovariance
namespace OAI
noncomputable section
open Set MeasureTheory
namespace PettyProjection
/-- The exact unrestricted inequality and its global equality characterization.
-/
theorem petty_projection_volume (n : ℕ) (hn : 4 ≤ n)
(K : Set (Space n)) (hK : IsConvexBody K) :
pettyConstant n ≤ projectionRatio K ∧
(projectionRatio K = pettyConstant n ↔ IsEllipsoid K) := by
obtain ⟨hbound,hrigid⟩ := projection_lower_bound hn hK
exact ⟨hbound,hrigid,ellipsoid_projectionRatio (by omega)⟩
theorem mainClaim_proved : MainClaim := petty_projection_volume
theorem MainClaim_proved : MainClaim := mainClaim_proved
end PettyProjection
end
end OAI
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