Hyperbolic mean curvature flow

DOI10.1016/j.jde.2008.06.026zbMath1159.53024arXiv1004.2754OpenAlexW2963589548WikidataQ125600676 ScholiaQ125600676MaRDI QIDQ2378198

De-Xing Kong, Chun-Lei He, Ke Feng Liu

Publication date: 7 January 2009

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

Full work available at URL: https://arxiv.org/abs/1004.2754

zbMATH Keywords

nonlinear stabilityhyperbolic mean curvature flowshort-time existence

Mathematics Subject Classification ID

Related Items (21)

Optimal System and Invariant Solutions of the Hyperbolic Geometric Flow ⋮ Symmetries and solutions of hyperbolic mean curvature flow with a constant forcing term ⋮ The motion of closed hypersurfaces in the central force fields ⋮ Formation of singularities in the motion of plane curves under hyperbolic mean curvature flow ⋮ Hyperbolic mean curvature flow in Minkowski space ⋮ A dissipative hyperbolic affine curve flow ⋮ Einstein's hyperbolic geometric flow ⋮ A nonexistence result for a nonlinear wave equation with damping on a Riemannian manifold ⋮ 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 ⋮ Hyperbolic inverse mean curvature flow ⋮ Invariant solutions of the normal hyperbolic mean curvature flow with dissipation ⋮ Hyperbolic curve flows in the plane ⋮ Nonlinear stability of blow-up solutions to the hyperbolic mean curvature flow ⋮ A Class of Second-Order Geometric Quasilinear Hyperbolic PDEs and Their Application in Imaging

Cites Work

• Unnamed Item
• Asymptotic behavior for singularities of the mean curvature flow
• The heat equation shrinking convex plane curves
• Lectures on nonlinear hyperbolic differential equations
• The inverse mean curvature flow and the Riemannian Penrose inequality
• Harnack estimate for the mean curvature flow
• Equations for the motion of relativistic torus in the Minkowski space R1+n
• Wave character of metrics and hyperbolic geometric flow
• Global solutions of nonlinear hyperbolic equations for small initial data
• Some regularity theorems in riemannian geometry
• A Hyperbolic Theory for the Evolution of Plane Curves
• Global existence for nonlinear wave equations
• Review of geometry and analysis

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