## Analysis & PDE

• Anal. PDE
• Volume 12, Number 3 (2019), 815-842.

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

#### 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.

#### Article information

Source
Anal. PDE, Volume 12, Number 3 (2019), 815-842.

Dates
Accepted: 29 June 2018
First available in Project Euclid: 25 October 2018

https://projecteuclid.org/euclid.apde/1540432871

Digital Object Identifier
doi:10.2140/apde.2019.12.815

Mathematical Reviews number (MathSciNet)
MR3864211

Zentralblatt MATH identifier
06986454

#### Citation

Rupflin, Melanie; Topping, Peter M. Global weak solutions of the Teichmüller harmonic map flow into general targets. Anal. PDE 12 (2019), no. 3, 815--842. doi:10.2140/apde.2019.12.815. https://projecteuclid.org/euclid.apde/1540432871

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