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Asymptotics of the Teichmüller harmonic map flow

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Rupflin, Melanie, Topping, Peter and Zhu, Miaomiao (2013) Asymptotics of the Teichmüller harmonic map flow. Advances in Mathematics, Volume 244 . pp. 874-893. doi:10.1016/j.aim.2013.05.021

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Official URL: http://dx.doi.org/10.1016/j.aim.2013.05.021

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Abstract

The Teichmüller harmonic map flow, introduced by Rupflin and Topping (2012) [11], evolves both a map from a closed Riemann surface to an arbitrary compact Riemannian manifold, and a constant curvature metric on the domain, in order to reduce its harmonic map energy as quickly as possible. In this paper, we develop the geometric analysis of holomorphic quadratic differentials in order to explain what happens in the case that the domain metric of the flow degenerates at infinite time. We obtain a branched minimal immersion from the degenerate domain.

Item Type: Journal Article
Divisions: Faculty of Science > Mathematics
Journal or Publication Title: Advances in Mathematics
Publisher: Academic Press
ISSN: 0001-8708
Official Date: 10 September 2013
Dates:
DateEvent
10 September 2013Published
Volume: Volume 244
Page Range: pp. 874-893
DOI: 10.1016/j.aim.2013.05.021
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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