Hyperbolic mean curvature flow: evolution of plane curves

DOI10.1016/S0252-9602(09)60049-7zbMATH Open1212.58018arXiv0803.0408OpenAlexW1932771679MaRDI QIDQ979442

Zenggui Wang, Kefeng Liu, De-Xing Kong

Publication date: 8 July 2010

Published in: Acta Mathematica Scientia. Series B. (English Edition) (Search for Journal in Brave)

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 $mathbb{R}^{1,1}$.

Full work available at URL: https://arxiv.org/abs/0803.0408

zbMATH Keywords

hyperbolic mean curvature flowhyperbolic Monge-Ampère equationshort-time existenceclosed plane curve

Mathematics Subject Classification ID

Hyperbolic equations on manifolds (58J45) Propagation of singularities; initial value problems on manifolds (58J47)

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