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...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Oxford University Press
2018
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| _version_ | 1826285170674630656 |
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| author | Cavalletti, F Mondino, A |
| author_facet | Cavalletti, F Mondino, A |
| author_sort | Cavalletti, F |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T01:24:50Z |
| format | Journal article |
| id | oxford-uuid:919b99ad-3fc6-4bd6-8ce5-b959e9d335a3 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:24:50Z |
| publishDate | 2018 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | oxford-uuid:919b99ad-3fc6-4bd6-8ce5-b959e9d335a32022-03-26T23:19:54ZAlmost euclidean isoperimetric inequalities in spaces satisfying local Ricci curvature lower boundsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:919b99ad-3fc6-4bd6-8ce5-b959e9d335a3EnglishSymplectic Elements at OxfordOxford University Press2018Cavalletti, FMondino, AMotivated 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. |
| spellingShingle | Cavalletti, F Mondino, A Almost euclidean isoperimetric inequalities in spaces satisfying local Ricci curvature lower bounds |
| title | Almost euclidean isoperimetric inequalities in spaces satisfying local Ricci curvature lower bounds |
| title_full | Almost euclidean isoperimetric inequalities in spaces satisfying local Ricci curvature lower bounds |
| title_fullStr | Almost euclidean isoperimetric inequalities in spaces satisfying local Ricci curvature lower bounds |
| title_full_unstemmed | Almost euclidean isoperimetric inequalities in spaces satisfying local Ricci curvature lower bounds |
| title_short | Almost euclidean isoperimetric inequalities in spaces satisfying local Ricci curvature lower bounds |
| title_sort | almost euclidean isoperimetric inequalities in spaces satisfying local ricci curvature lower bounds |
| work_keys_str_mv | AT cavallettif almosteuclideanisoperimetricinequalitiesinspacessatisfyinglocalriccicurvaturelowerbounds AT mondinoa almosteuclideanisoperimetricinequalitiesinspacessatisfyinglocalriccicurvaturelowerbounds |