Hyperbolic mean curvature flow

Chun-Lei He De-Xing Kong Kefeng Liu

Geometric Analysis and Geometric Topology mathscidoc:1912.43062

Journal of Differential Equations, 246, (1), 373-390, 2009.1
In this paper we introduce the hyperbolic mean curvature flow and prove that the corresponding system of partial differential equations is strictly hyperbolic, and based on this, we show that this flow admits a unique short-time smooth solution and possesses the nonlinear stability defined on the Euclidean space with dimension larger than 4. We derive nonlinear wave equations satisfied by some geometric quantities related to the hyperbolic mean curvature flow. Moreover, we also discuss the relation between the equations for hyperbolic mean curvature flow and the equations for extremal surfaces in the Minkowski spacetime.
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  title={Hyperbolic mean curvature flow},
  author={Chun-Lei He, De-Xing Kong, and Kefeng Liu},
  booktitle={Journal of Differential Equations},
Chun-Lei He, De-Xing Kong, and Kefeng Liu. Hyperbolic mean curvature flow. 2009. Vol. 246. In Journal of Differential Equations. pp.373-390. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111327463570622.
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