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2019 Global weak solutions of the Teichmüller harmonic map flow into general targets
Melanie Rupflin, Peter M. Topping
Anal. PDE 12(3): 815-842 (2019). DOI: 10.2140/apde.2019.12.815

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. "Global weak solutions of the Teichmüller harmonic map flow into general targets." Anal. PDE 12 (3) 815 - 842, 2019. https://doi.org/10.2140/apde.2019.12.815

Information

Received: 19 December 2017; Accepted: 29 June 2018; Published: 2019
First available in Project Euclid: 25 October 2018

zbMATH: 06986454
MathSciNet: MR3864211
Digital Object Identifier: 10.2140/apde.2019.12.815

Subjects:
Primary: 53A10, 53C43, 53C44

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 3 • 2019
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