The first variation of the total mass of log-concave functions and related inequalities

DOI10.1016/j.aim.2013.05.015zbMath1305.26033arXiv1112.2555OpenAlexW2031698393MaRDI QIDQ2437426

Ilaria Fragalà, Andrea Colesanti

Publication date: 3 March 2014

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

Full work available at URL: https://arxiv.org/abs/1112.2555

zbMATH Keywords

isoperimetric inequalityconvex bodieslog-Sobolev inequalitylog-concave functionsarea measureMinkowski's problem

Mathematics Subject Classification ID

Convexity of real functions of several variables, generalizations (26B25) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (27)

LYZ ellipsoid and Petty projection body for log-concave functions ⋮ Rogers-Shephard inequality for log-concave functions ⋮ John's ellipsoid and the integral ratio of a log-concave function ⋮ A homogeneous decomposition theorem for valuations on convex functions ⋮ On the framework of \(L_p\) summations for functions ⋮ Minkowski valuations on convex functions ⋮ \textit{A priori} bounds, existence, and uniqueness of smooth solutions to an anisotropic \(L_p\) Minkowski problem for log-concave measure ⋮ Projection body and isoperimetric inequalities for \(s\)-concave functions ⋮ Functional geominimal surface area and its related affine isoperimetric inequality ⋮ Quermassintegrals of quasi-concave functions and generalized Prékopa-Leindler inequalities ⋮ Equivariant endomorphisms of convex functions ⋮ Volume, polar volume and Euler characteristic for convex functions ⋮ On mixed quermassintegral for log-concave functions ⋮ Invariant Valuations on Super-Coercive Convex Functions ⋮ Hessian valuations ⋮ Monotone valuations on the space of convex functions ⋮ Valuations on log-concave functions ⋮ MORE ON LOGARITHMIC SUMS OF CONVEX BODIES ⋮ Best approximation of functions by log-polynomials ⋮ The functional inequality for the mixed quermassintegral ⋮ On $L_p$-Brunn-Minkowski type and $L_p$-isoperimetric type inequalities for measures ⋮ A Riesz representation theorem for functionals on log-concave functions ⋮ The Busemann-Petty problem on entropy of log-concave functions ⋮ Surface area measures of log-concave functions ⋮ Moment measures ⋮ 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

• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• A direct proof of the functional Santaló inequality
• Critères de convexité et inégalités intégrales
• Isoperimetric and analytic inequalities for log-concave probability measures
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• Mixed integrals and related inequalities
• \(\alpha\)-concave functions and a functional extension of mixed volumes
• Some functional forms of Blaschke-Santaló inequality
• Quermassintegrals of quasi-concave functions and generalized Prékopa-Leindler inequalities
• Geometry of log-concave functions and measures
• The case of equality for an inverse Santaló functional inequality
• Logarithmic Sobolev Inequalities
• The Brunn-Minkowski inequality
• On the Mean Width of Log-Concave Functions
• Marginals of Geometric Inequalities
• The Santaló point of a function, and a functional form of the Santaló inequality
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