A special case of Mahler's conjecture

DOI10.1007/PL00000076zbMath0916.52003OpenAlexW2025133954WikidataQ123195235 ScholiaQ123195235MaRDI QIDQ1275656

Mario A. Lopez, Shlomo Reisner

Publication date: 13 January 1999

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

Full work available at URL: https://doi.org/10.1007/pl00000076

zbMATH Keywords

Mahler's conjecturevolume productpolar convex body

Mathematics Subject Classification ID

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

Related Items (9)

The Mahler Conjecture in Two Dimensions via the Probabilistic Method ⋮ Stochastic reverse isoperimetric inequalities in the plane ⋮ Symmetric Mahler's conjecture for the volume product in the \(3\)-dimensional case ⋮ Geometry and volume product of finite dimensional Lipschitz-free spaces ⋮ The equipartition of curves ⋮ Stability of the reverse Blaschke-Santaló inequality for zonoids and applications ⋮ Heights on groups and small multiplicative dependencies ⋮ Mahler's conjecture for some hyperplane sections ⋮ Blaschke–Santaló and Mahler inequalities for the first eigenvalue of the Dirichlet Laplacian

Uses Software

• LEDA

Cites Work

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• Zonoids with minimal volume-product
• Une caractérisation volumique de certains espaces normés de dimension finie. (A volume characterization of some finite dimensional normed spaces)
• New volume ratio properties for convex symmetric bodies in \({\mathbb{R}}^ n\)
• Mahler's conjecture and wavelets
• Minimal Volume-Product in Banach Spaces with a 1-Unconditional Basis
• Cube Slicing in R n
• A Volume Inequality Concerning Sections of Convex Sets
• Zonoids with Minimal Volume-Product--A New Proof
• Spline Notation Applied to a Volume Problem
• A theorem on transfer for convex bodies
• A Theorem on Convex Bodies of the Brunn-Minkowski Type

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