Mean curvature flow of area decreasing maps between Riemann surfaces

Andreas Savas-Halilaj; Knut Smoczyk

Mean curvature flow of area decreasing maps between Riemann surfaces

Differential Geometry 2016-02-25 v1

Authors: Andreas Savas-Halilaj , Knut Smoczyk

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 $\min\sigma_M\ge\sup\sigma_N$ .

Keywords

mean curvature flow area decreasing maps Riemann surfaces bounded geometry sectional curvature evolution differential geometry

Cite

@article{arxiv.1602.07595,
  title  = {Mean curvature flow of area decreasing maps between Riemann surfaces},
  author = {Andreas Savas-Halilaj and Knut Smoczyk},
  journal= {arXiv preprint arXiv:1602.07595},
  year   = {2016}
}

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