Asymmetric Blaschke-Santaló functional inequalities

DOI10.1016/j.jfa.2019.108319zbMath1431.52005arXiv1810.02288OpenAlexW2975115190MaRDI QIDQ2007969

Marcos Montenegro, Carlos Hugo Jiménez, Julian Haddad

Publication date: 22 November 2019

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

Full work available at URL: https://arxiv.org/abs/1810.02288

zbMATH Keywords

momentconvex bodyfunctional inequalityBlaschke-Santaló inequalitySantaló pointRényi entropy

Mathematics Subject Classification ID

Measures of information, entropy (94A17) Convexity of real functions in one variable, generalizations (26A51) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (11)

Minimization to the Zhang's energy on \(BV (\Omega)\) and sharp affine Poincaré-Sobolev inequalities ⋮ On the L _p -sine moment-entropy inequality ⋮ Fixed point theorem: variants, affine context and some consequences ⋮ Spherical centroid bodies ⋮ Towards existence theorems to affine \(p\)-Laplace equations via variational approach ⋮ Equivariant endomorphisms of convex functions ⋮ On mixed quermassintegral for log-concave functions ⋮ A simple proof of the moment-entropy inequalities ⋮ A convex body associated to the Busemann random simplex inequality and the Petty conjecture ⋮ The functional inequality for the mixed quermassintegral ⋮ Sharp affine Trudinger–Moser inequalities: A new argument

Cites Work

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• Sharp affine Sobolev type inequalities via the \(L_{p}\) Busemann-Petty centroid inequality
• New approach to the affine Pólya-Szegö principle and the stability version of the affine Sobolev inequality
• Rogers-Shephard inequality for log-concave functions
• The Orlicz centroid inequality for star bodies
• An asymmetric affine Pólya-Szegő principle
• The sharp affine \(L^2\) Sobolev trace inequality and variants
• General \(L_{p}\) affine isoperimetric inequalities
• Orlicz projection bodies
• Contributions to affine surface area
• Blaschke-Santaló inequalities
• A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities.
• The affine Sobolev inequality.
• \(L_ p\) affine isoperimetric inequalities.
• LYZ ellipsoid and Petty projection body for log-concave functions
• Sharp affine \(L_ p\) Sobolev inequalities.
• Moment-entropy inequalities.
• Some functional forms of Blaschke-Santaló inequality
• Asymmetric affine \(L_p\) Sobolev inequalities
• Forward and reverse entropy power inequalities in convex geometry
• Quermassintegrals of quasi-concave functions and generalized Prékopa-Leindler inequalities
• An isoperimetric inequality for uniformly log-concave measures and uniformly convex bodies
• A degree theory for a class of perturbed Fredholm maps
• Geometry of log-concave functions and measures
• On the Blaschke-Santaló inequality
• Functional Versions ofL_p-Affine Surface Area and Entropy Inequalities
• A Fourier analytic proof of the Blaschke-Santaló Inequality
• Shadow Systems and Volumes of Polar Convex Bodies
• On the Discrete FunctionalL_pMinkowski Problem
• Logarithmically concave functions and sections of convex sets in $R^{n}$
• The Santaló-regions of a convex body
• Zhang’s Inequality for Log-Concave Functions
• On the functional Blaschke-Santaló inequality
• Sharp affine weighted 𝐿^{𝑝} Sobolev type inequalities
• Minkowski valuations
• The Santaló point of a function, and a functional form of the Santaló inequality

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