Stability of some versions of the Pr\'ekopa-Leindler inequality
K\'aroly J. B\"or\"oczky, Keith M. Ball
TL;DR
This paper presents stability results for the Prékopa-Leindler inequality, including its implications for the Blaschke-Santaló inequality and extensions to higher dimensions for even functions, utilizing recent stability results of the Brunn-Minkowski inequality.
Contribution
It provides new stability versions of the Prékopa-Leindler inequality and related inequalities, extending known results to higher dimensions and even functions.
Findings
Stability version of the Blaschke-Santaló inequality.
Stability version of the Prékopa-Leindler inequality for even functions in higher dimensions.
Utilization of recent stability results of the Brunn-Minkowski inequality.
Abstract
Two consequences of the stability version of the one dimensional Pr\'ekopa-Leindler inequality are presented. One is the stability version of the Blaschke-Santal\'o inequality, and the other is a stability version of the Pr\'ekopa-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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Taxonomy
TopicsPoint processes and geometric inequalities · Geometric Analysis and Curvature Flows · Mathematics and Applications