2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147022We 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.39 pagesProbabilityMetric Geometrytext