Stability of some versions of the Prékopa-Leindler inequality

2009/09/21 by Károly J. Böröczky, Keith Ball, Böröczky, Károly J. +2 · 3 citations
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities #Probability (math.PR) #math.MG #math.PR

paper · pdf · doi:10.48550/arxiv.0909.3742

arxiv created 2009/09/21 · openalex publication_date 2009/09/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Two consequences of the stability version of the one dimensional Prékopa-Leindler inequality are presented. One is the stability version of the Blaschke-Santaló inequality, and the other is a stability version of the Prékopa-Leindler inequality for even functions in higher dimensions, where a recent stability version of the Brunn-Minkowski inequality is also used in an essential way.

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• Sharp stability in hypercontractivity estimates and logarithmic Sobolev inequalities
• A parabolic PDE-based approach to Borell–Brascamp–Lieb inequality
• Quantitative Borell-Brascamp-Lieb inequalities for compactly supported power concave functions (and some applications)

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• A quantitative stability result for the Prékopa-Leindler inequality for arbitrary measurable functions
• Some extensions of the Pr 'ekopa-Leindler inequality using Borell's\n stochastic approach