An isoperimetric inequality for uniformly log-concave measures and uniformly convex bodies

Details An isoperimetric inequality for uniformly log-concave measures and uniformly convex bodies An isoperimetric inequality for uniformly log-concave measures and uniformly convex bodies

2007-03-28

arxiv.org/abs/math/0703857v2

J. Funct. Anal., vol. 254, issue 5 (2008), pp 1235-1268

Mathematics

Probability

39 pages

Scientific paper

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.

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