John's ellipsoid and the integral ratio of a log-concave function

DOI10.1007/s12220-017-9858-4zbMath1406.52011arXiv1511.01266OpenAlexW2963050440MaRDI QIDQ1651364

Bernardo González Merino, Rafael Villa, David Alonso-Gutiérrez, Carlos Hugo Jiménez

Publication date: 12 July 2018

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.01266

zbMATH Keywords

volume ratiolog-concave functionJohn positionreverse affine isoperimetric inequality

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21) Asymptotic theory of convex bodies (52A23)

Related Items (16)

LYZ ellipsoid and Petty projection body for log-concave functions ⋮ The Löwner function of a log-concave function ⋮ Minkowski valuations on convex functions ⋮ Some remarks on petty projection of log-concave functions ⋮ Zhang’s Inequality for Log-Concave Functions ⋮ On mixed quermassintegral for log-concave functions ⋮ Functional Löwner ellipsoids ⋮ From affine Poincaré inequalities to affine spectral inequalities ⋮ An extension of Berwald's inequality and its relation to Zhang's inequality ⋮ Best approximation of functions by log-polynomials ⋮ Rogers-Shephard and local Loomis-Whitney type inequalities ⋮ The functional inequality for the mixed quermassintegral ⋮ The Busemann-Petty problem on entropy of log-concave functions ⋮ Geometry of log-concave functions: the \(L_p\) Asplund sum and the \(L_p\) Minkowski problem ⋮ Affine invariant maps for log-concave functions ⋮ Functional John ellipsoids

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