LOCAL MINIMALITY OF THE VOLUME‐PRODUCT AT THE SIMPLEX

DOI10.1112/S0025579310001555zbMath1226.52002arXiv1001.0217MaRDI QIDQ3074008

Jaegil Kim, Shlomo Reisner

Publication date: 14 February 2011

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.0217

zbMATH Keywords

convex bodyMahler conjecturevolume-productBlaschke-Santalo inequalityBanach-Mazur space

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Length, area, volume and convex sets (aspects of convex geometry) (52A38)

Related Items (16)

On convex intersection bodies and unique determination problems for convex bodies ⋮ Minimal volume product of three dimensional convex bodies with various discrete symmetries ⋮ Stochastic reverse isoperimetric inequalities in the plane ⋮ Symmetric Mahler's conjecture for the volume product in the \(3\)-dimensional case ⋮ Shadow systems of asymmetric \(L_p\) zonotopes ⋮ Volume inequalities for Orlicz zonotopes ⋮ A generalized rotationally symmetric case of the centroaffine Minkowski problem ⋮ A remark on rotationally symmetric solutions to the centroaffine Minkowski problem ⋮ On the volume product of polygons ⋮ Minimal volume product near Hanner polytopes ⋮ Volume inequalities for asymmetric Orlicz zonotopes ⋮ Stability of the reverse Blaschke-Santaló inequality for unconditional convex bodies ⋮ An application of shadow systems to Mahler's conjecture ⋮ Blaschke–Santaló and Mahler inequalities for the first eigenvalue of the Dirichlet Laplacian ⋮ Polytopes of maximal volume product ⋮ On the shape of a convex body with respect to its second projection body

Cites Work

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• A remark on the Mahler conjecture: local minimality of the unit cube
• Stability of the reverse Blaschke-Santaló inequality for zonoids and applications
• From the Mahler conjecture to Gauss linking integrals
• 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 and Volumes of Polar Convex Bodies
• Minimal Volume-Product in Banach Spaces with a 1-Unconditional Basis
• The Santaló-regions of a convex body

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