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Embedded area-constrained Willmore tori of small area in Riemannian three-manifolds I: minimization

Abstract:

We construct embedded Willmore tori with small area constraint in Riemannian three-manifolds under some curvature condition used to prevent Möbius degeneration. The construction relies on a Lyapunov-Schmidt reduction; to this aim we establish new geometric expansions of exponentiated small symmetric Clifford tori and analyze the sharp asymptotic behaviour of degenerating tori under the action of the Möbius group. In this first work we prove two existence results by minimizing or maximizing a ...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1112/plms.12047

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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:
London Mathematical Society Publisher's website
Journal:
Proceedings of the London Mathematical Society Journal website
Volume:
115
Issue:
3
Pages:
502-544
Publication date:
2017-06-07
Acceptance date:
2017-05-04
DOI:
EISSN:
1460-244X
ISSN:
0024-6115
Source identifiers:
1061591
Language:
English
Keywords:
Pubs id:
pubs:1061591
UUID:
uuid:5c4b62aa-b812-447d-b1ca-6696a7967bec
Local pid:
pubs:1061591
Deposit date:
2019-10-11

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