A quantitative stability result for the Pr\'ekopa-Leindler inequality for arbitrary measurable functions
Functional Analysis
2022-01-28 v1 Metric Geometry
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.
Cite
@article{arxiv.2201.11564,
title = {A quantitative stability result for the Pr\'ekopa-Leindler inequality for arbitrary measurable functions},
author = {Károly J. Böröczky and Alessio Figalli and João P. G. Ramos},
journal= {arXiv preprint arXiv:2201.11564},
year = {2022}
}
Comments
37 pages, 0 figures