Functional Brunn-Minkowski inequalities induced by polarity

DOI10.1016/j.aim.2020.107006zbMath1439.44005arXiv1707.08732OpenAlexW3004684836MaRDI QIDQ2302233

Dan I. Florentin, Shiri Artstein-Avidan, Alexander Segal

Publication date: 25 February 2020

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

Full work available at URL: https://arxiv.org/abs/1707.08732

zbMATH Keywords

interpolationconvex functionsintegral inequalitiesBrunn-Minkowski inequalityconcave functionalsinfimum convolution

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Inequalities and extremum problems involving convexity in convex geometry (52A40) Mixed volumes and related topics in convex geometry (52A39)

Related Items (9)

The equality cases in Steiner's projection inequality ⋮ On the framework of \(L_p\) summations for functions ⋮ On a geometric combination of functions related to Prékopa–Leindler inequality ⋮ On Prékopa-Leindler type inequality for Sugeno integral ⋮ A zoo of dualities ⋮ On the Linear Structures Induced by the Four Order Isomorphisms Acting on ${\rm{Cvx}}_0({\mathbb R}^n)$ ⋮ A Santaló-type inequality for the 𝒥 transform ⋮ Best approximation of functions by log-polynomials ⋮ Geometry of log-concave functions: the \(L_p\) Asplund sum and the \(L_p\) Minkowski problem

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• Differential analysis of polarity: polar Hamilton-Jacobi, conservation laws, and Monge Ampère equations
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• Logarithmically concave functions and sections of convex sets in $R^{n}$
• The Brunn-Minkowski inequality
• Asymptotic Geometric Analysis, Part I
• A Theorem on Convex Bodies of the Brunn-Minkowski Type

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