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Mean Curvature Flows of Lagrangian Submanifolds with Convex Potentials

Knut Smoczyk Leibniz University of Hanover Mu-Tao Wang Columbia University

Differential Geometry mathscidoc:1608.10067

Journal of Differential Geometry, 62, (2), 243-257, 2002
This article studies the mean curvature flow of Lagrangian submanifolds. In particular, we prove the following global existence and convergence theorem: if the potential function of a Lagrangian graph in $T^{2n}$ is convex, then the flow exists for all time and converges smoothly to a flat Lagrangian submanifold. We also discuss various conditions on the potential function that guarantee global existence and convergence.
Mean Curvature Flow, Lagrangian Submanifolds
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@inproceedings{knut2002mean,
  title={Mean Curvature Flows of Lagrangian Submanifolds with Convex Potentials },
  author={Knut Smoczyk, and Mu-Tao Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160822221710851152384},
  booktitle={Journal of Differential Geometry},
  volume={62},
  number={2},
  pages={243-257},
  year={2002},
}
Knut Smoczyk, and Mu-Tao Wang. Mean Curvature Flows of Lagrangian Submanifolds with Convex Potentials . 2002. Vol. 62. In Journal of Differential Geometry. pp.243-257. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160822221710851152384.
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