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Foliation by area-constrained Willmore spheres near a non-degenerate critical point of the scalar curvature

Abstract:

Let $(M,g)$ be a 3-dimensional Riemannian manifold. The goal of the paper it to show that if $P_{0}\in M$ is a non-degenerate critical point of the scalar curvature, then a neighborhood of $P_{0}$ is foliated by area-constrained Willmore spheres. Such a foliation is unique among foliations by area-constrained Willmore spheres having Willmore energy less than $32\pi$, moreover it is regular in the sense that a suitable rescaling smoothly converges to a round sphere in the Euclidean three-dimen...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1093/imrn/rny203

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Institution:
University of Oxford
Department:
Mathematical Institute
Oxford college:
St Hilda's College
Role:
Author
ORCID:
0000-0002-1932-7148
Publisher:
Oxford University Press Publisher's website
Journal:
International Mathematics Research Notices Journal website
Volume:
2020
Issue:
19
Pages:
6539–6568
Publication date:
2018-08-31
Acceptance date:
2018-08-06
DOI:
EISSN:
1687-0247
ISSN:
1073-7928
Source identifiers:
1061629
Language:
English
Keywords:
Pubs id:
pubs:1061629
UUID:
uuid:fae122a4-0298-4037-838e-f36024171d5c
Local pid:
pubs:1061629
Deposit date:
2019-10-11

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