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.
"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