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Hyper-Lagrangian submanifolds of hyperkahler manifolds and mean curvature flow

Conan Leung Chinese Univ of HK Tom Wan Chinese Univ of HK

Differential Geometry mathscidoc:1608.10090

Journal Geom Analy, 17, (2), 343-364, 2007
In this article, we define a new class of middle dimensional submanifolds of a Hyperkahler manifold which contains the class of complex Lagrangian submanifolds, and show that this larger class is invariant under the mean curvature flow. Along the flow, the complex phase map satisfies the generalized harmonic map heat equation, tt is also related to the mean curvature vector via a first order differential equation. Moreover, we proved a result on nonexistence of Type I singularity.
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[ Download ] [ 2016-08-31 10:33:54 uploaded by conan ] [ 549 downloads ] [ 0 comments ] [ Cited by 1 ] 
@inproceedings{conan2007hyper-lagrangian,
  title={Hyper-Lagrangian submanifolds of hyperkahler manifolds and mean curvature flow},
  author={Conan Leung, and Tom Wan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160831103354921244566},
  booktitle={Journal Geom Analy},
  volume={17},
  number={2},
  pages={343-364},
  year={2007},
}
Conan Leung, and Tom Wan. Hyper-Lagrangian submanifolds of hyperkahler manifolds and mean curvature flow. 2007. Vol. 17. In Journal Geom Analy. pp.343-364. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160831103354921244566.
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