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arXiv · 1709.01881

Global weak solutions of the Teichmüller harmonic map flow into general targets

Melanie Rupflin·Peter M. Topping
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Abstract

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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Melanie Rupflin, Peter M. Topping. 2017-09-06. Global weak solutions of the Teichmüller harmonic map flow into general targets. https://doi.org/10.2140/apde.2019.12.815

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