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arXiv · 2201.11564

A quantitative stability result for the Pr\'ekopa-Leindler inequality for arbitrary measurable functions

Károly J. Böröczky·Alessio Figalli·João P. G. Ramos
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Abstract

We prove that if a triplet of functions satisfies almost equality in the Pr\'ekopa-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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Károly J. Böröczky, Alessio Figalli, João P. G. Ramos. 2022-01-27. A quantitative stability result for the Pr\'ekopa-Leindler inequality for arbitrary measurable functions. https://arxiv.org/abs/2201.11564

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