Mean Curvature Flows and Isotopy of Maps Between Spheres

Mu-Tao Wang Columbia University

Differential Geometry mathscidoc:1608.10060

Communications on Pure and Applied Mathematics, 57, (8), 1110-1126., 2004
Let $f$ be a smooth map between unit spheres of possibly different dimensions. We prove the global existence and convergence of the mean curvature flow of the graph of $f$ under various conditions. A corollary is that any area-decreasing map between unit spheres (of possibly different dimensions) is isotopic to a constant map.
Mean Curvature Flows
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@inproceedings{mu-tao2004mean,
  title={Mean Curvature Flows and Isotopy of Maps Between Spheres},
  author={Mu-Tao Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160821234337208767374},
  booktitle={Communications on Pure and Applied Mathematics},
  volume={57},
  number={8},
  pages={1110-1126.},
  year={2004},
}
Mu-Tao Wang. Mean Curvature Flows and Isotopy of Maps Between Spheres. 2004. Vol. 57. In Communications on Pure and Applied Mathematics. pp.1110-1126.. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160821234337208767374.
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