Hyperbolic mean curvature flow: Evolution of plane curves

Details Hyperbolic mean curvature flow: Evolution of plane curves Hyperbolic mean curvature flow: Evolution of plane curves

2008-03-04

arxiv.org/abs/0803.0408v1

Mathematics

Differential Geometry

26 pages

Scientific paper

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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