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Embedded area-constrained Willmore tori of small area in Riemannian three-manifolds, II: Morse Theory

Abstract:

This is the second part of a series of two papers where we construct embedded Willmore tori with small area constraint in Riemannian three-manifolds. In both papers the construction relies on a Lyapunov-Schmidt reduction, the difficulty being the Mübius degeneration of the tori. In the first paper the construction was performed via minimization, here by Morse Theory. To this aim we establish new geometric expansions of the derivative of the Willmore functional on small Clifford tori (in geode...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1353/ajm.2017.0033

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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:
Johns Hopkins University Press Publisher's website
Journal:
American Journal of Mathematics Journal website
Volume:
139
Issue:
5
Pages:
1315-1378
Publication date:
2017-10-01
Acceptance date:
2016-09-06
DOI:
EISSN:
1080-6377
ISSN:
0002-9327
Source identifiers:
1061590
Language:
English
Keywords:
Pubs id:
pubs:1061590
UUID:
uuid:43e25e42-bf09-4f10-b003-009342f0b4e4
Local pid:
pubs:1061590
Deposit date:
2019-10-11

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