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A frame energy for immersed tori and applications to regular homotopy classes

Abstract:

The paper is devoted to studying the Dirichlet energy of moving frames on 2-dimensional tori immersed in the euclidean 3 ≤ m-dimensional space. This functional, called frame energy, is naturally linked to the Willmore energy of the immersion and on the conformal structure of the abstract underlying surface. As the first result, a Willmore-conjecture type lower bound is established: namely for every torus immersed in ℝm, m ≥ 3, and any moving frame on it, the frame energy is at least 2π2 and e...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.4310/jdg/1473186541

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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:
International Press Publisher's website
Journal:
Journal of Differential Geometry Journal website
Volume:
104
Issue:
1
Pages:
143-186
Publication date:
2016-09-06
Acceptance date:
2015-11-04
DOI:
EISSN:
1945-743X
ISSN:
0022-040X
Source identifiers:
1061601
Language:
English
Keywords:
Pubs id:
pubs:1061601
UUID:
uuid:69ac60e1-514d-4cb4-a9c7-a9fded5b07ec
Local pid:
pubs:1061601
Deposit date:
2019-10-11

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