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Refined asymptotics of the Teichmuller harmonic map flow into general targets
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Huxol, Tobias, Rupflin, Melanie and Topping, Peter (2016) Refined asymptotics of the Teichmuller harmonic map flow into general targets. Calculus of Variations and Partial Differential Equations, 55 (85). doi:10.1007/s00526-016-1019-2 ISSN 0944-2669.
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Official URL: http://link.springer.com/journal/526
Abstract
The Teichmüller harmonic map flow is a gradient flow for the harmonic map energy of maps from a closed surface to a general closed Riemannian target manifold of any dimension, where both the map and the domain metric are allowed to evolve. Given a weak solution of the flow that exists for all time t ≥ 0, we find a sequence of times ti → ∞ at which the flow at different scales converges to a collection of branched minimal immersions with no loss of energy. We do this by developing a compactness theory, establishing no loss of energy, for sequences of almost-minimal maps. Moreover, we construct an example of a smooth flow for which the image of the limit branched minimal immersions is disconnected. In general, we show that the necks connecting the images of the branched minimal immersions become arbitrarily thin as i → ∞.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Teichmüller spaces, Riemannian manifolds | ||||||||
| Journal or Publication Title: | Calculus of Variations and Partial Differential Equations | ||||||||
| Publisher: | Springer | ||||||||
| ISSN: | 0944-2669 | ||||||||
| Official Date: | August 2016 | ||||||||
| Dates: |
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| Volume: | 55 | ||||||||
| Number: | 85 | ||||||||
| DOI: | 10.1007/s00526-016-1019-2 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 14 June 2016 | ||||||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||||||
| Grant number: | EP/K00865X/1. | ||||||||
| Related URLs: | |||||||||
| Open Access Version: |
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