A quantitative stability result for the Prékopa-Leindler inequality for arbitrary measurable functions
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE(2024)
Abstract
We prove that if a triplet of functions satisfies almost -equality in the Pr & eacute;kopa-Leindler inequality, then these functions are close to a common log -concave function, up to multiplication and rescaling. Our result holds for general measurable functions in all dimensions, and provides a quantitative stability estimate with computable constants.
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Key words
Pr & eacute,kopa-Leindler inequality,stability,Brunn-Minkowski inequality
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