Stability of the Pr\'ekopa-Leindler inequality
K\'aroly J. B\"or\"oczky, Keith M. Ball
TL;DR
This paper establishes a stability version of the Prékopa-Leindler inequality, providing insights into how small deviations affect the inequality's bounds in convex analysis.
Contribution
It introduces a stability result for the Prékopa-Leindler inequality, enhancing understanding of its robustness under perturbations.
Findings
Proved a quantitative stability estimate.
Identified conditions under which the inequality remains nearly tight.
Extended the inequality's applicability to approximate cases.
Abstract
We prove a stability version of the Pr\'ekopa-Leindler inequality.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Geometric and Algebraic Topology