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Rearrangement and Prekopa-Leindler type inequalities (1806.08837v2)
Published 22 Jun 2018 in math.PR, cs.IT, math.FA, and math.IT
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.