Vol. 12, No. 3, 2019

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

Melanie Rupflin and Peter M. Topping

Vol. 12 (2019), No. 3, 815–842
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.

Keywords
geometric flows, minimal surfaces, harmonic maps
Mathematical Subject Classification 2010
Primary: 53A10, 53C43, 53C44
Milestones
Received: 19 December 2017
Accepted: 29 June 2018
Published: 7 October 2018
Authors
Melanie Rupflin
Mathematical Institute
University of Oxford
Oxford
United Kingdom
Peter M. Topping
Mathematics Institute
University of Warwick
Coventry
United Kingdom