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Teichmüller harmonic map flow into nonpositively curved targets

Abstract:

The Teichmüller harmonic map flow deforms both a map from an oriented closed surface M into an arbitrary closed Riemannian manifold, and a constant curvature metric on M, so as to reduce the energy of the map as quickly as possible [16]. The flow then tries to converge to a branched minimal immersion when it can [16, 18]. The only thing that can stop the flow is a finite-time degeneration of the metric on M where one or more collars are pinched. In this paper we show that finite-time degenera...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.4310/jdg/1513998032

Authors


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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Institute
Topping, PM More by this author
Publisher:
International Press Publisher's website
Journal:
Journal of Differential Geometry Journal website
Volume:
108
Issue:
1
Pages:
135-184
Publication date:
2017-12-23
Acceptance date:
2016-02-01
DOI:
EISSN:
1945-743X
ISSN:
0022-040X
URN:
uuid:d0654a7b-b10b-4725-98e9-9fd184314b9c
Source identifiers:
611158
Local pid:
pubs:611158

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