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Isoperimetric inequality under Measure-Contraction property

TitleIsoperimetric inequality under Measure-Contraction property
Publication TypeJournal Article
Year of Publication2019
AuthorsCavalletti, F, Santarcangelo, F
Pagination2893 - 2917
Date Published2019/11/01/
ISBN Number0022-1236
KeywordsIsoperimetric inequality; Measure-Contraction property; Optimal transport; Ricci curvature

We prove that if (X,d,m) is an essentially non-branching metric measure space with m(X)=1, having Ricci curvature bounded from below by K and dimension bounded above by N∈(1,∞), understood as a synthetic condition called Measure-Contraction property, then a sharp isoperimetric inequality à la Lévy-Gromov holds true. Measure theoretic rigidity is also obtained.

Short TitleJournal of Functional Analysis

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