Analysis & PDE

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

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

Melanie Rupflin and Peter M. Topping

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42] 53C43: Differential geometric aspects of harmonic maps [See also 58E20] 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)

geometric flows minimal surfaces harmonic maps


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.

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