Hyperbolic mean curvature flow: Evolution of plane curves

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dc.creatorKong, De-Xing
dc.creatorLiu, Kefeng
dc.creatorWang, Zeng-Gui
dc.date2008-03-04
dc.date.accessioned2026-07-07T09:24:33Z
dc.date.available2026-07-07T09:24:33Z
dc.descriptionIn 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 $\mathbb{R}^{1,1}$.
dc.description26 pages
dc.identifierhttps://arxiv.org/abs/0803.0408
dc.identifierhttp://arxiv.org/abs/0803.0408
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/156133
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.titleHyperbolic mean curvature flow: Evolution of plane curves
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