JournalsaihpcVol. 41, No. 3pp. 565–614

A quantitative stability result for the Prékopa–Leindler inequality for arbitrary measurable functions

  • Károly J. Böröczky

    Alfréd Rényi Institute of Mathematics, Budapest, Hungary

  • Alessio Figalli

    ETH Zürich, Switzerland

  • João P. G. Ramos

    ETH Zurich, Switzerland
A quantitative stability result for the Prékopa–Leindler inequality for arbitrary measurable functions cover
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Abstract

We prove that if a triplet of functions satisfies almost-equality in the Prékopa–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.

Cite this article

Károly J. Böröczky, Alessio Figalli, João P. G. Ramos, A quantitative stability result for the Prékopa–Leindler inequality for arbitrary measurable functions. Ann. Inst. H. Poincaré Anal. Non Linéaire 41 (2024), no. 3, pp. 565–614

DOI 10.4171/AIHPC/97