Hyperbolic mean curvature flow: evolution of plane curves

Kong Dexing Kefeng Liu Wang Zenggui

Geometric Analysis and Geometric Topology mathscidoc:1912.43059

Acta Mathematica Scientia, 29, (3), 493-514, 2009.5
In this paper we investigate the one-dimensional hyperbolic mean curvature flow for closed plane curves. More precisely, we consider a family of closed curves S 1[0, T) 2 which satisfies the following evolution equation 2 F t 2 (u, t)= k (u, t) N(u, t)- (u, t),(u, t) S 1[0, T) with the initial data F (u, 0)= F 0 (u) a n d F t (u, 0)= f (u) N 0, where k is the mean curvature and is the unit inner normal vector of the plane curve F (u, t), f (u) and are the initial velocity and the unit inner normal vector of the initial convex closed curve Fo, respectively, and is given by ( 2 F s t, F t) T, in which stands for the unit tangent vector. The above problem is an initial value problem for a system of partial differential equations for F, it can be completely reduced to an initial value problem for a single partial differential equation for its support function. The latter equation is a hyperbolic Monge-Ampere
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@inproceedings{kong2009hyperbolic,
  title={Hyperbolic mean curvature flow: evolution of plane curves},
  author={Kong Dexing, Kefeng Liu, and Wang Zenggui},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111315878202619},
  booktitle={Acta Mathematica Scientia},
  volume={29},
  number={3},
  pages={493-514},
  year={2009},
}
Kong Dexing, Kefeng Liu, and Wang Zenggui. Hyperbolic mean curvature flow: evolution of plane curves. 2009. Vol. 29. In Acta Mathematica Scientia. pp.493-514. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111315878202619.
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