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,...
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| Format: | Journal article |
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Mathematical Sciences Publishers
2018
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| Summary: | 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. |
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