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Finite‐time degeneration for variants of Teichmüller harmonic map flow

Abstract:

We consider the question of whether solutions of variants of Teichmüller harmonic map flow from surfaces 𝑀 to general targets can degenerate in finite time. For the original flow from closed surfaces of genus at least 2, as well as the flow from cylinders, we prove that such a finite‐time degeneration must occur in situations where the image of thin collars is ‘stretching out’ at a rate of at least inj(𝑀,𝑔)−(14+𝛿) , and we construct targets in which the flow from cylinders must indeed dege...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1112/jlms.12327

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
London Mathematical Society
Journal:
Journal of the London Mathematical Society More from this journal
Volume:
102
Issue:
2
Pages:
535-556
Publication date:
2020-05-05
Acceptance date:
2020-01-31
DOI:
ISSN:
0024-6107
Language:
English
Keywords:
Pubs id:
1087022
Local pid:
pubs:1087022
Deposit date:
2020-02-12

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