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

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dc.creatorMilman, Emanuel
dc.creatorSodin, Sasha
dc.date2007-03-28
dc.date2007-11-21
dc.date.accessioned2026-07-07T08:57:35Z
dc.date.available2026-07-07T08:57:35Z
dc.descriptionWe 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.
dc.description39 pages
dc.identifierhttps://arxiv.org/abs/math/0703857
dc.identifierhttp://arxiv.org/abs/math/0703857
dc.identifierJ. Funct. Anal., vol. 254, issue 5 (2008), pp 1235-1268
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/147022
dc.subjectProbability
dc.subjectMetric Geometry
dc.titleAn isoperimetric inequality for uniformly log-concave measures and uniformly convex bodies
dc.typetext

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