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Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds

Abstract:

We prove that if (X, d, m) is a metric measure space with m(X) = 1 having (in a synthetic sense) Ricci curvature bounded from below by K> 0 and dimension bounded above by N∈ [1 , ∞) , then the classic Lévy-Gromov isoperimetric inequality (together with the recent sharpening counterparts proved in the smooth setting by Milman for any K∈ R, N≥ 1 and upper diameter bounds) holds, i.e. the isoperimetric profile function of (X, d, m) is bounded from below by the isoperimetric profile of the mod...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s00222-016-0700-6

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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:
Springer
Journal:
Inventiones Mathematicae More from this journal
Volume:
208
Issue:
3
Pages:
803-849
Publication date:
2016-11-19
Acceptance date:
2016-10-23
DOI:
EISSN:
1432-1297
ISSN:
0020-9910
Language:
English
Keywords:
Pubs id:
pubs:1061613
UUID:
uuid:d35de02f-00fc-4f2a-a7ee-9b959253d9f5
Local pid:
pubs:1061613
Source identifiers:
1061613
Deposit date:
2019-10-11

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