Motivated by Perelman's Pseudo Locality Theorem for the Ricci flow, we prove that if a Riemannian manifold has Ricci curvature bounded below in a metric ball which moreover has almost maximal volume, then in a smaller ball (in a quantified sense) it holds an almost-euclidean isoperimetric inequality. The result is actually established in the more general framework of non-smooth spaces satisfying local Ricci curvature lower bounds in a synthetic sense via optimal transportation.

Almost Euclidean Isoperimetric Inequalities in Spaces Satisfying Local Ricci Curvature Lower Bounds / Cavalletti, F.; Mondino, A.. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 2020:5(2020), pp. 1481-1510. [10.1093/imrn/rny070]

Almost Euclidean Isoperimetric Inequalities in Spaces Satisfying Local Ricci Curvature Lower Bounds

Cavalletti, F.;
2020

Abstract

Motivated by Perelman's Pseudo Locality Theorem for the Ricci flow, we prove that if a Riemannian manifold has Ricci curvature bounded below in a metric ball which moreover has almost maximal volume, then in a smaller ball (in a quantified sense) it holds an almost-euclidean isoperimetric inequality. The result is actually established in the more general framework of non-smooth spaces satisfying local Ricci curvature lower bounds in a synthetic sense via optimal transportation.
2020
5
1481
1510
https://academic.oup.com/imrn/article/2020/5/1481/4971297
https://arxiv.org/abs/1703.02119
Cavalletti, F.; Mondino, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/85650
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