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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
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: |
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| 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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