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Global weak solutions
of the Teichmüller harmonic map flow into general targets
Melanie Rupflin and Peter M. Topping |
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Vol. 12 (2019), No. 3, 815–842
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Abstract |
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We analyse finite-time singularities of the Teichmüller 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 no-loss-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. |
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Keywords
geometric flows, minimal surfaces, harmonic maps
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Mathematical Subject Classification 2010
Primary: 53A10, 53C43, 53C44
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Milestones
Received: 19 December 2017
Accepted: 29 June 2018
Published: 7 October 2018
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Authors |
| Melanie Rupflin | |
| Mathematical Institute University of Oxford Oxford United Kingdom |
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| Peter M. Topping | |
| Mathematics Institute University of Warwick Coventry United Kingdom |
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