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.

References in corpus (1)

• Horizontal curves of hyperbolic metrics

Cited by in corpus (3)

• A new conformal heat flow of harmonic maps
• Plateau flow or the heat flow for half-harmonic maps
• Finite-time degeneration for variants of Teichmüller harmonic map flow