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...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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De Gruyter
2020
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| _version_ | 1797108595586760704 |
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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 |