Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality

DOI10.1016/j.jfa.2012.02.014zbMath1255.52010arXiv1110.5551OpenAlexW1985301162MaRDI QIDQ418724

Carsten Schuett, Shiri Artstein-Avidan, Elisabeth M. Werner, Bo'az Klartag

Publication date: 30 May 2012

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.5551

zbMATH Keywords

logarithmic Sobolev inequalitylog-concave functions\(s\)-concave functionsaffine isoperimetric inequality

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Inequalities for sums, series and integrals (26D15)

Related Items (31)

LYZ ellipsoid and Petty projection body for log-concave functions ⋮ The spherical convex floating body ⋮ Rogers-Shephard inequality for log-concave functions ⋮ John's ellipsoid and the integral ratio of a log-concave function ⋮ The equality cases in Steiner's projection inequality ⋮ The Löwner function of a log-concave function ⋮ Constrained convex bodies with extremal affine surface areas ⋮ Floating functions ⋮ Continuity of the solution to the \(L_p\) Minkowski problem in Gaussian probability space ⋮ Projection body and isoperimetric inequalities for \(s\)-concave functions ⋮ Functional geominimal surface area and its related affine isoperimetric inequality ⋮ A Stein deficit for the logarithmic Sobolev inequality ⋮ Divergence for \(s\)-concave and log concave functions ⋮ On mixed quermassintegral for log-concave functions ⋮ Stability of the logarithmic Sobolev inequality via the Föllmer process ⋮ The mixed L_p affine surface areas for functions ⋮ A stochastic Prékopa–Leindler inequality for log-concave functions ⋮ A sharp symmetrized form of Talagrand's transport-entropy inequality for the Gaussian measure ⋮ Halfspace depth and floating body ⋮ Mixedf-divergence and inequalities for log-concave functions ⋮ Flag numbers and floating bodies ⋮ Affine isoperimetric inequalities in the functional Orlicz-Brunn-Minkowski theory ⋮ Ulam floating bodies ⋮ Orlicz Addition for Measures and an Optimization Problem for the -divergence ⋮ 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 ⋮ Pinsker inequalities and related Monge-Ampere equations for 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

Cites Work

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