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Rigidity for critical points in the Lévy-Gromov inequality

Abstract:
The Lévy-Gromov inequality states that round spheres have the least isoperimetric profile (normalized by total volume) among Riemannian manifolds with a fixed positive lower bound on the Ricci tensor. In this note we study critical metrics corresponding to the Lévy-Gromov inequality and prove that, in two-dimensions, this criticality condition is quite rigid, as it characterizes round spheres and projective planes.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s00209-017-1993-x

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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 Publisher's website
Journal:
Mathematische Zeitschrift Journal website
Volume:
289
Issue:
3-4
Pages:
1191-1197
Publication date:
2017-12-07
Acceptance date:
2017-10-14
DOI:
EISSN:
1432-1823
ISSN:
0025-5874
Source identifiers:
1061588
Language:
English
Keywords:
Pubs id:
pubs:1061588
UUID:
uuid:7762b322-c980-4dcb-9b26-53bb3fab8519
Local pid:
pubs:1061588
Deposit date:
2019-10-11

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