Formation of singularities in the motion of plane curves under hyperbolic mean curvature flow

DOI10.1016/j.jde.2009.04.016zbMath1195.53093OpenAlexW1992680517MaRDI QIDQ842890

Zenggui Wang, De-Xing Kong

Publication date: 28 September 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2009.04.016

zbMATH Keywords

curvatureblowuphyperbolic flow

Mathematics Subject Classification ID

Related Items (14)

Optimal System and Invariant Solutions of the Hyperbolic Geometric Flow ⋮ The motion of closed hypersurfaces in the central force fields ⋮ Hyperbolic mean curvature flow in Minkowski space ⋮ A dissipative hyperbolic affine curve flow ⋮ Wave-type threshold dynamics and the hyperbolic mean curvature flow ⋮ Life-span of classical solutions to hyperbolic inverse mean curvature flow ⋮ Hyperbolic inverse mean curvature flow with forced term: Evolution of plane curves ⋮ Symmetries and conservation laws associated with a hyperbolic mean curvature flow ⋮ Dissipative hyperbolic mean curvature flow for closed convex plane curves ⋮ Discrete Hyperbolic Curvature Flow in the Plane ⋮ Hyperbolic mean curvature flow for Lagrangian graphs: one dimensional case ⋮ Hyperbolic mean curvature flow with a forcing term: evolution of plane curves ⋮ The evolutionary properties on solitary solutions of nonlinear evolution equations ⋮ Invariant solutions of the normal hyperbolic mean curvature flow with dissipation

Cites Work

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• Shortening embedded curves
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• Convexity estimates for mean curvature flow and singularities of mean convex surfaces
• Hyperbolic mean curvature flow
• The hyperbolic mean curvature flow
• Hyperbolic systems of conservation laws II
• Formation of singularities for nonlinear hyperbolic partial differential equations
• Formation of singularities for wave equations including the nonlinear vibrating string
• Some regularity theorems in riemannian geometry
• A Hyperbolic Theory for the Evolution of Plane Curves
• Formation and propagation of singularities for $2\times 2$ quasilinear hyperbolic systems
• Blow up of periodic solutions to quasilinear hyperbolic systems
• Review of geometry and analysis

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