Rogers-Shephard inequality for log-concave functions
Functional Analysis
2016-09-14 v2 Metric Geometry
Abstract
In this paper we prove different functional inequalities extending the classical Rogers-Shephard inequalities for convex bodies. The original inequalities provide an optimal relation between the volume of a convex body and the volume of several symmetrizations of the body, such as, its difference body. We characterize the equality cases in all these inequalities. Our method is based on the extension of the notion of a convolution body of two convex sets to any pair of log-concave functions and the study of some geometrical properties of these new sets.
Keywords
Cite
@article{arxiv.1410.2556,
title = {Rogers-Shephard inequality for log-concave functions},
author = {David Alonso-Gutiérrez and Bernardo González Merino and C. Hugo Jiménez and Rafael Villa},
journal= {arXiv preprint arXiv:1410.2556},
year = {2016}
}
Comments
25 pages