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Quantitative isoperimetry à la Levy-Gromov

Abstract:

On a Riemannian manifold with a positive lower bound on the Ricci tensor, the distance of isoperimetric sets from geodesic balls is quantitatively controlled in terms of the gap between the isoperimetric profile of the manifold and that of a round sphere of suitable radius. The deficit between the diameters of the manifold and of the corresponding sphere is likewise bounded. These results are actually obtained in the more general context of (possibly nonsmooth) metric measure spaces with curv...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1002/cpa.21808

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
St Hilda's College
Role:
Author
ORCID:
0000-0002-1932-7148
Publisher:
Wiley Publisher's website
Journal:
Communications on Pure and Applied Mathematics Journal website
Volume:
72
Issue:
8
Pages:
1631-1677
Publication date:
2018-12-22
Acceptance date:
2018-07-11
DOI:
EISSN:
1097-0312
ISSN:
0010-3640
Source identifiers:
1061627
Keywords:
Pubs id:
pubs:1061627
UUID:
uuid:98bf14d4-f280-4115-882c-8828a9e8d3ce
Local pid:
pubs:1061627
Deposit date:
2019-10-11

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