Global weak solutions of the Teichmüller harmonic map flow into general targets
We analyse finite-time singularities of the Teichm¨uller harmonic map flow – a natural gradient flow of the harmonic map energy – and find a canonical way of flowing beyond them in order to construct global solutions in full generality. Moreover, we prove a noloss-of-topology result at finite time,...
| Autori principali: | , |
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| Natura: | Journal article |
| Pubblicazione: |
Mathematical Sciences Publishers
2018
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| _version_ | 1826307172684791808 |
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| author | Rupflin, ME Topping, PM |
| author_facet | Rupflin, ME Topping, PM |
| author_sort | Rupflin, ME |
| collection | OXFORD |
| description | We analyse finite-time singularities of the Teichm¨uller harmonic map flow – a natural gradient flow of the harmonic map energy – and find a canonical way of flowing beyond them in order to construct global solutions in full generality. Moreover, we prove a noloss-of-topology result at finite time, which completes the proof that this flow decomposes an arbitrary map into a collection of branched minimal immersions connected by curves. |
| first_indexed | 2024-03-07T06:58:57Z |
| format | Journal article |
| id | oxford-uuid:ff1505ee-a6e3-4a18-bb31-5ee5a3d48186 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:58:57Z |
| publishDate | 2018 |
| publisher | Mathematical Sciences Publishers |
| record_format | dspace |
| spelling | oxford-uuid:ff1505ee-a6e3-4a18-bb31-5ee5a3d481862022-03-27T13:41:47ZGlobal weak solutions of the Teichmüller harmonic map flow into general targetsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:ff1505ee-a6e3-4a18-bb31-5ee5a3d48186Symplectic Elements at OxfordMathematical Sciences Publishers2018Rupflin, METopping, PMWe analyse finite-time singularities of the Teichm¨uller harmonic map flow – a natural gradient flow of the harmonic map energy – and find a canonical way of flowing beyond them in order to construct global solutions in full generality. Moreover, we prove a noloss-of-topology result at finite time, which completes the proof that this flow decomposes an arbitrary map into a collection of branched minimal immersions connected by curves. |
| spellingShingle | Rupflin, ME Topping, PM Global weak solutions of the Teichmüller harmonic map flow into general targets |
| title | Global weak solutions of the Teichmüller harmonic map flow into general targets |
| title_full | Global weak solutions of the Teichmüller harmonic map flow into general targets |
| title_fullStr | Global weak solutions of the Teichmüller harmonic map flow into general targets |
| title_full_unstemmed | Global weak solutions of the Teichmüller harmonic map flow into general targets |
| title_short | Global weak solutions of the Teichmüller harmonic map flow into general targets |
| title_sort | global weak solutions of the teichmuller harmonic map flow into general targets |
| work_keys_str_mv | AT rupflinme globalweaksolutionsoftheteichmullerharmonicmapflowintogeneraltargets AT toppingpm globalweaksolutionsoftheteichmullerharmonicmapflowintogeneraltargets |