Almost euclidean isoperimetric inequalities in spaces satisfying local Ricci curvature lower bounds
- 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.
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- Peer reviewed
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- Cavalletti and Mondino
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- © The Author(s) 2018. Published by Oxford University Press.
- This is the accepted manuscript version of the article. The final version is available online from Oxford University Press at: 10.1093/imrn/rny070
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