An isoperimetric inequality for uniformly log-concave measures and uniformly convex bodies
Probability
2008-02-01 v2 Metric Geometry
Abstract
We prove an isoperimetric inequality for the uniform measure on a uniformly convex body and for a class of uniformly log-concave measures (that we introduce). These inequalities imply (up to universal constants) the log-Sobolev inequalities proved by Bobkov--Ledoux as well as the isoperimetric inequalities due to Bakry-Ledoux and Bobkov--Zegarlinski. We also recover a concentration inequality for uniformly convex bodies, similar to that proved by Gromov--Milman.
Keywords
Cite
@article{arxiv.math/0703857,
title = {An isoperimetric inequality for uniformly log-concave measures and uniformly convex bodies},
author = {Emanuel Milman and Sasha Sodin},
journal= {arXiv preprint arXiv:math/0703857},
year = {2008}
}
Comments
39 pages