Cavalletti, Fabio and Mondino, Andrea (2018) Almost euclidean isoperimetric inequalities in spaces satisfying local Ricci curvature lower bounds. International Mathematics Research Notices . doi:10.1093/imrn/rny070 ISSN 1687-0247.

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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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Ricci flow, Riemannian manifolds, Isoperimetric inequalities
Journal or Publication Title:	International Mathematics Research Notices
Publisher:	Oxford University Press
ISSN:	1687-0247
Official Date:	16 April 2018
Dates:	Date Event 16 April 2018 Available 23 March 2018 Accepted
DOI:	10.1093/imrn/rny070
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	11 April 2018
Date of first compliant Open Access:	16 April 2019
Related URLs:	Publisher

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