Curvature Decay Estimates of Graphical Mean Curvature Flow in Higher Codimensions

Knut Smoczyk Leibniz Universit├Ąt Hannover Mao-Pei Tsui University of Toledo Mu-Tao Wang Columbia University

Differential Geometry Geometric Analysis and Geometric Topology mathscidoc:1608.10018

Transactions of the American Mathematical Society, 2016.1
We derive pointwise curvature estimates for graphical mean curvature flows in higher codimensions. To the best of our knowledge, this is the first such estimates without assuming smallness of first derivatives of the defining map. An immediate application is a convergence theorem of the mean curvature flow of the graph of an area decreasing map between flat Riemann surfaces.
Curvature Decay Estimates, Mean Curvature Flow, Riemann surfaces
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@inproceedings{knut2016curvature,
  title={Curvature Decay Estimates of Graphical Mean Curvature Flow in Higher Codimensions},
  author={Knut Smoczyk, Mao-Pei Tsui, and Mu-Tao Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160820150415523185322},
  booktitle={Transactions of the American Mathematical Society},
  year={2016},
}
Knut Smoczyk, Mao-Pei Tsui, and Mu-Tao Wang. Curvature Decay Estimates of Graphical Mean Curvature Flow in Higher Codimensions. 2016. In Transactions of the American Mathematical Society. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160820150415523185322.
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