Uniqueness and nonuniqueness of limits of Teichmüller harmonic map flow
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 conver...
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Format: | Journal article |
Language: | English |
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De Gruyter
2020
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author | Kohout, J Rupflin, M Topping, PM |
author_facet | Kohout, J Rupflin, M Topping, PM |
author_sort | Kohout, J |
collection | OXFORD |
description | 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 t→∞. |
first_indexed | 2024-03-07T07:29:30Z |
format | Journal article |
id | oxford-uuid:da44cde0-2221-4b54-aa4b-2dbc7cad8359 |
institution | University of Oxford |
language | English |
last_indexed | 2024-03-07T07:29:30Z |
publishDate | 2020 |
publisher | De Gruyter |
record_format | dspace |
spelling | oxford-uuid:da44cde0-2221-4b54-aa4b-2dbc7cad83592023-01-05T07:55:59ZUniqueness and nonuniqueness of limits of Teichmüller harmonic map flowJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:da44cde0-2221-4b54-aa4b-2dbc7cad8359EnglishSymplectic ElementsDe Gruyter2020Kohout, JRupflin, MTopping, PMThe 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 t→∞. |
spellingShingle | Kohout, J Rupflin, M Topping, PM Uniqueness and nonuniqueness of limits of Teichmüller harmonic map flow |
title | Uniqueness and nonuniqueness of limits of Teichmüller harmonic map flow |
title_full | Uniqueness and nonuniqueness of limits of Teichmüller harmonic map flow |
title_fullStr | Uniqueness and nonuniqueness of limits of Teichmüller harmonic map flow |
title_full_unstemmed | Uniqueness and nonuniqueness of limits of Teichmüller harmonic map flow |
title_short | Uniqueness and nonuniqueness of limits of Teichmüller harmonic map flow |
title_sort | uniqueness and nonuniqueness of limits of teichmuller harmonic map flow |
work_keys_str_mv | AT kohoutj uniquenessandnonuniquenessoflimitsofteichmullerharmonicmapflow AT rupflinm uniquenessandnonuniquenessoflimitsofteichmullerharmonicmapflow AT toppingpm uniquenessandnonuniquenessoflimitsofteichmullerharmonicmapflow |