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Asymptotics of the Teichmüller harmonic map flow

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Rupflin,  Melanie
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1209.3783
(Preprint), 270KB

AdvMath244_874.pdf
(Any fulltext), 263KB

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Citation

Rupflin, M., Topping, P. M., & Zhu, M. (2013). Asymptotics of the Teichmüller harmonic map flow. Advances in mathematics, 244, 874-893. doi:10.1016/j.aim.2013.05.021.


Cite as: https://hdl.handle.net/11858/00-001M-0000-000E-7C83-E
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.