Long-time existence and convergence of graphic mean curvature flow in arbitrary codimension

Mu-Tao Wang Columbia University

Differential Geometry mathscidoc:1608.10070

Inventiones mathematicae , 148, (3), 525-543, 2002
Let $ f : \sum_1 \to \sum_2$ be a map between compact Riemannian manifolds of constant curvature. This article considers the evolution of the graph of f in $\sum_1 \times \sum_2$2 by the mean curvature flow. Under suitable conditions on the curvature of $\sum_1$ and $\sum_2$ and the differential of the initial map, we show that the flow exists smoothly for all time. At each instant $t$, the flow remains the graph of a map $f_t$ and $f_t$ converges to a constant map as $t$ approaches infinity. This also provides a regularity estimate for Lipschtz initial data.
Riemannian manifolds, mean curvature flow, codimension
[ Download ] [ 2016-08-22 23:17:08 uploaded by mutaowang ] [ 753 downloads ] [ 0 comments ] [ Cited by 61 ]
@inproceedings{mu-tao2002long-time,
  title={Long-time existence and convergence of graphic mean curvature flow  in arbitrary codimension},
  author={Mu-Tao Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160822231708646403387},
  booktitle={Inventiones mathematicae },
  volume={148},
  number={3},
  pages={525-543},
  year={2002},
}
Mu-Tao Wang. Long-time existence and convergence of graphic mean curvature flow in arbitrary codimension. 2002. Vol. 148. In Inventiones mathematicae . pp.525-543. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160822231708646403387.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved