An application of shadow systems to Mahler's conjecture

DOI10.1007/s00454-012-9435-3zbMath1258.52006OpenAlexW2008114322WikidataQ123188905 ScholiaQ123188905MaRDI QIDQ714987

Mathieu Meyer, Matthieu Fradelizi, Artem Zvavitch

Publication date: 15 October 2012

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00454-012-9435-3

zbMATH Keywords

convex bodiesconvex polytopesSantaló pointvolume productpolar bodiesshadow systems

Mathematics Subject Classification ID

Three-dimensional polytopes (52B10) Inequalities and extremum problems involving convexity in convex geometry (52A40) Affine differential geometry (53A15)

Related Items (10)

Equipartitions and Mahler volumes of symmetric convex bodies ⋮ Minimal volume product of three dimensional convex bodies with various discrete symmetries ⋮ Symmetric Mahler's conjecture for the volume product in the \(3\)-dimensional case ⋮ Shadow systems of asymmetric \(L_p\) zonotopes ⋮ Sylvester-Busemann type functionals with respect to Orlicz centroid bodies ⋮ Geometry and volume product of finite dimensional Lipschitz-free spaces ⋮ Volume inequalities for asymmetric Orlicz zonotopes ⋮ Stability of the reverse Blaschke-Santaló inequality for unconditional convex bodies ⋮ Polytopes of maximal volume product ⋮ Volume inequalities for Orlicz mean bodies

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The isotropic position and the reverse Santaló inequality
• A remark on the Mahler conjecture: local minimality of the unit cube
• 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)
• The structure of finite dimensional Banach spaces with the 3.2. intersection property
• 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 \({\mathbb{R}}^ n\)
• The case of equality for an inverse Santaló functional inequality
• LOCAL MINIMALITY OF THE VOLUME‐PRODUCT AT THE SIMPLEX
• Mahler's Conjecture and Curvature
• Some extremal problems for convex bodies
• Shadow Systems and Volumes of Polar Convex Bodies
• Minimal Volume-Product in Banach Spaces with a 1-Unconditional Basis
• Zonoids with Minimal Volume-Product--A New Proof
• Approximation of Convex Bodies by Polytopes
• Convex Polytopes
• The Hörmander Proof of the Bourgain–Milman Theorem
• The volume product of convex bodies with many hyperplane symmetries
• On volume product inequalities for convex sets
• A theorem on transfer for convex bodies

This page was built for publication: An application of shadow systems to Mahler's conjecture