Asymptotics of the Teichm\"uller harmonic map flow
Differential Geometry
2012-09-19 v1 Analysis of PDEs
Abstract
The Teichm\"uller harmonic map flow, introduced in [9], evolves both a map from a closed Riemann surface to an arbitrary compact Riemannian manifold, and a constant curvature metric on the domain, in order to reduce its harmonic map energy as quickly as possible. In this paper, we develop the geometric analysis of holomorphic quadratic differentials in order to explain what happens in the case that the domain metric of the flow degenerates at infinite time. We obtain a branched minimal immersion from the degenerate domain.
Keywords
Cite
@article{arxiv.1209.3783,
title = {Asymptotics of the Teichm\"uller harmonic map flow},
author = {Melanie Rupflin and Peter M. Topping and Miaomiao Zhu},
journal= {arXiv preprint arXiv:1209.3783},
year = {2012}
}