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arXiv · 0803.0408

Hyperbolic mean curvature flow: Evolution of plane curves

De-Xing Kong·Kefeng Liu·Zeng-Gui Wang
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Abstract

In this paper we investigate the one-dimensional hyperbolic mean curvature flow for closed plane curves. We show that there exists a class of initial velocities such that the solution of the corresponding initial value problem exists only at a finite time interval $[0,T_{\max})$ and when $t$ goes to $T_{\max}$, the solution converges to a point. We also discuss the close relationship between the hyperbolic mean curvature flow and the equations for the evolving relativistic string in the Minkowski space-time $\mathbb{R}^{1,1}$.

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De-Xing Kong, Kefeng Liu, Zeng-Gui Wang. 2008-03-04. Hyperbolic mean curvature flow: Evolution of plane curves. https://arxiv.org/abs/0803.0408

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