The volume product of convex bodies with many hyperplane symmetries

DOI10.1353/ajm.2013.0018zbMath1277.52010OpenAlexW2107824891MaRDI QIDQ4917533

Matthieu Fradelizi, Franck Barthe

Publication date: 30 April 2013

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1353/ajm.2013.0018

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) Duality and reflexivity in normed linear and Banach spaces (46B10) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Symmetry properties of polytopes (52B15)

Related Items (22)

The Slicing Problem by Bourgain ⋮ Equipartitions and Mahler volumes of symmetric convex bodies ⋮ Isotropic constants and Mahler volumes ⋮ A SIMPLICIAL POLYTOPE THAT MAXIMIZES THE ISOTROPIC CONSTANT MUST BE A SIMPLEX ⋮ 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 ⋮ Log-Brunn-Minkowski inequality under symmetry ⋮ On a geometric combination of functions related to Prékopa–Leindler inequality ⋮ Volume inequalities for Orlicz zonotopes ⋮ Transport proofs of some functional inverse Santaló inequalities ⋮ Geometry and volume product of finite dimensional Lipschitz-free spaces ⋮ Minimal volume product near Hanner polytopes ⋮ A stochastic Prékopa–Leindler inequality for log-concave functions ⋮ Invariant Valuations on Super-Coercive Convex Functions ⋮ 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 ⋮ Stable solution of the Logarithmic Minkowski problem in the case of hyperplane symmetries ⋮ Polytopes of maximal volume product ⋮ On the shape of a convex body with respect to its second projection body

This page was built for publication: The volume product of convex bodies with many hyperplane symmetries