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Some rigidity results for the Hawking mass and a lower bound for the Bartnik capacity

Abstract:

We prove rigidity results involving the Hawking mass for surfaces immersed in a 3-dimensional, complete Riemannian manifold $(M,g)$ with non-negative scalar curvature (respectively, with scalar curvature bounded below by $-6$ ). Roughly, the main result states that if an open subset $\Omega \subset M$ satisfies that every point has a neighbourhood $U\subset \Omega$ such that the supremum of the Hawking mass of surfaces contained in $U$ is non-positive, then $\Omega$ is locally isometric to Eu...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1112/jlms.12612

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
St Hilda's College
Role:
Author
ORCID:
0000-0002-1932-7148
Publisher:
London Mathematical Society Publisher's website
Journal:
Journal of London Mathematical Society Journal website
Publication date:
2022-04-20
Acceptance date:
2022-02-04
DOI:
EISSN:
1469-7750
ISSN:
0024-6107
Language:
English
Keywords:
Pubs id:
1187786
Local pid:
pubs:1187786
Deposit date:
2022-02-06

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