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arXiv · 1806.08837

Rearrangement and Prekopa-Leindler type inequalities

James Melbourne
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Abstract

We investigate the interactions of functional rearrangements with Prekopa-Leindler type inequalities. It is shown that that a general class of integral inequalities tighten on rearrangement to "isoperimetric" sets with respect to a relevant measure. Applications to the Borell-Brascamp-Lieb, Borell-Ehrhart, and the recent polar Prekopa-Leindler inequalities are demonstrated. It is also proven that an integrated form of the Gaussian log-Sobolev inequality decreases on half-space rearrangement.

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James Melbourne. 2018-06-22. Rearrangement and Prekopa-Leindler type inequalities. https://arxiv.org/abs/1806.08837

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