A strong stability condition on minimal submanifolds and its implications

Chung-Jun Tsai National Taiwan University Mu-Tao Wang Columbia University

Analysis of PDEs Differential Geometry Geometric Analysis and Geometric Topology mathscidoc:1804.03010

We identify a strong stability condition on minimal submanifolds that implies uniqueness and dynamical stability properties. In particular, we prove a uniqueness theorem and a dynamical stability theorem of the mean curvature flow for minimal submanifolds that satisfy this condition. The latter theorem states that the mean curvature flow of any other submanifold in a neighborhood of such a minimal submanifold exists for all time, and converges exponentially to the minimal one. This extends our previous uniqueness and stability theorem which applies only to calibrated submanifolds of special holonomy ambient manifolds.
minimal submanifold, mean curvature flow
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  • arXiv: 1710.00433
@inproceedings{chung-juna,
  title={A strong stability condition on minimal submanifolds and its implications},
  author={Chung-Jun Tsai, and Mu-Tao Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180430143124249484081},
}
Chung-Jun Tsai, and Mu-Tao Wang. A strong stability condition on minimal submanifolds and its implications. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180430143124249484081.
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