Shadow Systems and Volumes of Polar Convex Bodies

DOI10.1112/S0025579300000061zbMath1118.52015arXivmath/0606305MaRDI QIDQ3433996

Mathieu Meyer, Shlomo Reisner

Publication date: 23 April 2007

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0606305

zbMATH Keywords

polytopesextremal problemsmixed volumesshadow systemsBlaschke-Santaló inequaliyexact reverse Santaló inequalitypolar convex bodies

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Mixed volumes and related topics in convex geometry (52A39) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (30)

On a non-homogeneous version of a problem of Firey ⋮ Equipartitions and Mahler volumes of symmetric convex bodies ⋮ On the sine polarity and the \(L_p\)-sine Blaschke-Santaló inequality ⋮ Stochastic reverse isoperimetric inequalities in the plane ⋮ Shadow systems of asymmetric \(L_p\) zonotopes ⋮ On the L _p -sine moment-entropy inequality ⋮ A sharp Rogers and Shephard inequality for the $p$-difference body of planar convex bodies ⋮ Sylvester-Busemann type functionals with respect to Orlicz centroid bodies ⋮ Sharp isoperimetric inequalities for affine quermassintegrals ⋮ The Grassmannian \(L_p\)-sine Blaschke-Santaló inequality ⋮ Shadow systems: remarks and extensions ⋮ Stability of the functional forms of the Blaschke-Santaló inequality ⋮ Stability of the Blaschke-Santaló and the affine isoperimetric inequality ⋮ Geometry and volume product of finite dimensional Lipschitz-free spaces ⋮ Volume inequalities for asymmetric Orlicz zonotopes ⋮ Stability of the reverse Blaschke-Santaló inequality for zonoids and applications ⋮ Stability of some versions of the Prékopa-Leindler inequality ⋮ Asymmetric Blaschke-Santaló functional inequalities ⋮ Stability of the reverse Blaschke-Santaló inequality for unconditional convex bodies ⋮ A sharp Rogers-Shephard type inequality for Orlicz-difference body of planar convex bodies ⋮ An application of shadow systems to Mahler's conjecture ⋮ Mahler's conjecture for some hyperplane sections ⋮ Strengthened inequalities for the mean width and the ℓ‐norm ⋮ Volume of the polar of random sets and shadow systems ⋮ LOCAL MINIMALITY OF THE VOLUME‐PRODUCT AT THE SIMPLEX ⋮ THE CONVEX INTERSECTION BODY OF A CONVEX BODY ⋮ ELLIPSOIDS ARE THE ONLY LOCAL MAXIMIZERS OF THE VOLUME PRODUCT ⋮ A reverse Blaschke-Santaló inequality ⋮ Polytopes of maximal volume product ⋮ Volume inequalities for Orlicz mean bodies

Cites Work

• Unnamed Item
• Zonoids with minimal volume-product
• Une caractérisation volumique de certains espaces normés de dimension finie. (A volume characterization of some finite dimensional normed spaces)
• Convex bodies with minimal volume product in \(\mathbb{R}^ 2\)
• Inequalities involving integrals of polar-conjugate concave functions
• New volume ratio properties for convex symmetric bodies in \({\mathbb{R}}^ n\)
• Shadow systems of convex sets
• On the Blaschke-Santaló inequality
• Minimal Volume-Product in Banach Spaces with a 1-Unconditional Basis
• Zonoids with Minimal Volume-Product--A New Proof
• On volume product inequalities for convex sets
• A Theorem on Convex Bodies of the Brunn-Minkowski Type

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