Support functions and mean width for \(\alpha\)-concave functions

DOI10.1016/j.aim.2013.03.023zbMath1296.26046arXiv1210.4340OpenAlexW2963888033MaRDI QIDQ392959

Liran Rotem

Publication date: 15 January 2014

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.4340

zbMATH Keywords

support functionmean width\(\alpha\)-concavitygeneralized Poincaré inequalitysup-convolution operationUrysohn type inequality

Mathematics Subject Classification ID

Convexity of real functions of several variables, generalizations (26B25) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (13)

LYZ ellipsoid and Petty projection body for log-concave functions ⋮ On the framework of \(L_p\) summations for functions ⋮ Projection body and isoperimetric inequalities for \(s\)-concave functions ⋮ Functional geominimal surface area and its related affine isoperimetric inequality ⋮ A sharp Blaschke-Santaló inequality for \(\alpha \)-concave functions ⋮ On mixed quermassintegral for log-concave functions ⋮ Best approximation of functions by log-polynomials ⋮ The functional inequality for the mixed quermassintegral ⋮ The functional form of the dual mixed volume ⋮ Dualities and endomorphisms of pseudo-cones ⋮ The Busemann-Petty problem on entropy of log-concave functions ⋮ Surface area measures of log-concave functions ⋮ Geometry of log-concave functions: the \(L_p\) Asplund sum and the \(L_p\) Minkowski problem

Cites Work

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• Geometry of log-concave functions and measures
• Interpolations, Convexity and Geometric Inequalities
• On the Mean Width of Log-Concave Functions
• r-convex functions

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