Mean curvature flow of area decreasing maps between Riemann surfaces

Andreas Savas-Halilaj; Knut Smoczyk

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arXiv · 1602.07595

Mean curvature flow of area decreasing maps between Riemann surfaces

Andreas Savas-Halilaj·Knut Smoczyk

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Abstract

In this article we give a complete description of the evolution of an area decreasing map $f:M\to N$ induced by its mean curvature in the situation where $M$ and $N$ are complete Riemann surfaces with bounded geometry, $M$ being compact, for which their sectional curvatures $\sigma_M$, $\sigma_N$ satisfy $\min\sigma_M\ge\sup\sigma_N$.

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Andreas Savas-Halilaj, Knut Smoczyk. 2016-02-24. Mean curvature flow of area decreasing maps between Riemann surfaces. https://arxiv.org/abs/1602.07595

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