On $L_p$-Brunn-Minkowski type and $L_p$-isoperimetric type inequalities for measures

DOI10.1090/tran/8356zbMath1465.52021arXiv2004.09737OpenAlexW3110657852MaRDI QIDQ4992381

Sudan Xing, Michael Roysdon

Publication date: 8 June 2021

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.09737

zbMATH Keywords

\(L_p\)-Brunn-Minkowski inequality\(L_p\)-Borell-Brascamp-Lieb inequality\(L_p\)-isoperimetric inequality\(L_p\)-Prékopa-Leindler inequality

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Length, area, volume, other geometric measure theory (28A75) Mixed volumes and related topics in convex geometry (52A39)

Related Items (6)

Existence of solution for Lp-Minkowski problem of 0 < p < 1 with measures in ℝn ⋮ Weighted Minkowski’s existence theorem and projection bodies ⋮ Notes on the log-Brunn-Minkowski inequality ⋮ On the framework of \(L_p\) summations for functions ⋮ On discrete \(L_p\) Brunn-Minkowski type inequalities ⋮ The \(L_p\) John ellipsoids for general measures

Cites Work

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• The Brunn-Minkowski-Firey inequality for nonconvex sets
• The log-Brunn-Minkowski inequality
• A note on an \(L^p\)-Brunn-Minkowski inequality for convex measures in the unconditional case
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• The logarithmic Minkowski inequality for non-symmetric convex bodies
• Convex set functions in d-space
• On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
• A flow approach to the fractional Minkowski problem
• Brunn-Minkowski inequalities in product metric measure spaces
• A unified treatment for \(L_p\) Brunn-Minkowski type inequalities
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• The \(L_p\)-Brunn-Minkowski inequality for \(p<1\)
• The dimensional Brunn-Minkowski inequality in Gauss space
• Rogers-Shephard type inequalities for sections
• An extension of Minkowski's theorem and its applications to questions about projections for measures
• Affine images of isotropic measures
• The \(L_p\) Minkowski problem for polytopes for \(0 < p < 1\)
• The planar \(L_{p}\)-Minkowski problem for \(0<p<1\)
• On the stability of Brunn-Minkowski type inequalities
• A generalization of \(L_{p}\)-Brunn-Minkowski inequalities and \(L_{p}\)-Minkowski problems for measures
• Convex bodies and norms associated to convex measures
• Quermassintegrals of quasi-concave functions and generalized Prékopa-Leindler inequalities
• The first variation of the total mass of log-concave functions and related inequalities
• Remarks on the conjectured log-Brunn-Minkowski inequality
• Geometry of log-concave functions and measures
• On the improvement of concavity of convex measures
• On the Discrete Logarithmic Minkowski Problem
• MORE ON LOGARITHMIC SUMS OF CONVEX BODIES
• A note on a Brunn-Minkowski inequality for the Gaussian measure
• Gaussian Brunn-Minkowski inequalities
• Logarithmically concave functions and sections of convex sets in $R^{n}$
• The Brunn-Minkowski inequality
• The logarithmic Minkowski problem
• On the Local Version of the Log-Brunn–Minkowski Conjecture and Some New Related Geometric Inequalities
• Stability for a strengthened Borell–Brascamp–Lieb inequality
• The log-Brunn-Minkowski inequality in ℝ³
• Asymptotic Geometric Analysis, Part I
• On the Brunn-Minkowski inequality for general measures with applications to new isoperimetric-type inequalities
• Convex Bodies The Brunn-MinkowskiTheory
• Marginals of Geometric Inequalities
• $p$-Means of Convex Bodies.

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