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Uniqueness and nonuniqueness of limits of teichmuller harmonic map flow
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Kohout, James, Rupflin, Melanie and Topping, Peter (2022) Uniqueness and nonuniqueness of limits of teichmuller harmonic map flow. Advances in Calculus of Variations, 15 (3). pp. 369-384. doi:10.1515/acv-2019-0086 ISSN 1864-8258.
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Official URL: https://doi.org/10.1515/acv-2019-0086
Abstract
The harmonic map energy of a map from a closed, constant-curvature surface to a closed target manifold can be seen as a functional on the space of maps and domain metrics. We consider the gradient flow for this energy. In the absence of singularities, previous theory established that the flow converges to a branched minimal immersion, but only at a sequence of times converging to infinity, and only after pulling back by a sequence of diffeomorphisms. In this paper, we investigate whether it is necessary to pull back by these diffeomorphisms, and whether the convergence is uniform as
| 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): | Calculus, Teichmüller spaces, Harmonic maps, Conjugate gradient methods, Singularities (Mathematics) | |||||||||
| Journal or Publication Title: | Advances in Calculus of Variations | |||||||||
| Publisher: | Walter de Gruyter GmbH & Co. KG | |||||||||
| ISSN: | 1864-8258 | |||||||||
| Official Date: | 2022 | |||||||||
| Dates: |
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| Volume: | 15 | |||||||||
| Number: | 3 | |||||||||
| Page Range: | pp. 369-384 | |||||||||
| DOI: | 10.1515/acv-2019-0086 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||
| Date of first compliant deposit: | 11 February 2020 | |||||||||
| Date of first compliant Open Access: | 24 February 2021 | |||||||||
| RIOXX Funder/Project Grant: |
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