Global weak solutions of the Teichm\"uller harmonic map flow into general targets
Differential Geometry
2018-10-17 v1 Analysis of PDEs
Abstract
We analyse finite-time singularities of the Teichm\"uller 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
Cite
@article{arxiv.1709.01881,
title = {Global weak solutions of the Teichm\"uller harmonic map flow into general targets},
author = {Melanie Rupflin and Peter M. Topping},
journal= {arXiv preprint arXiv:1709.01881},
year = {2018}
}