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.;
2020-01-01
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.File | Dimensione | Formato | |
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