Convex curves moving translationally in the plane

DOI10.1016/J.JDE.2006.03.005zbMath1098.35080OpenAlexW1964085926MaRDI QIDQ2496740

Dong-Ho Tsai, Chia-Hsing Nien

Publication date: 20 July 2006

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

Full work available at URL: https://doi.org/10.1016/j.jde.2006.03.005

zbMATH Keywords

curvature flowhomothetic self-similar solutiontranslational self-similar solution

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Initial value problems for second-order parabolic equations (35K15) Curves in Euclidean and related spaces (53A04)

Related Items (8)

Affine self-similar solutions of the affine curve shortening flow. I: The degenerate case ⋮ Generalized elastic translating solitons ⋮ The blow up analysis of the general curve shortening flow ⋮ Symmetry reductions and exact solutions of the affine heat equation ⋮ On a nonlinear parabolic equation arising from anisotropic plane curve evolution ⋮ Blow-up rates for the general curve shortening flow ⋮ Evolving a convex closed curve to another one via a length-preserving linear flow ⋮ Contracting convex immersed closed plane curves with slow speed of curvature

Cites Work

• Unnamed Item
• Geometric expansion of convex plane curves
• On the formation of singularities in the curve shortening flow
• Asymptotic behaviors of star-shaped curves expanding by \(V=1-K\).
• The normalized curve shortening flow and homothetic solutions
• The heat equation shrinking convex plane curves
• The heat equation shrinks embedded plane curves to round points
• Correction to: ``An expansion of convex hypersurfaces
• Evolving convex curves
• Geometric aspects of Aleksandrov reflection and gradient estimates for parabolic equations
• A logarithmic Gauss curvature flow and the Minkowski problem.
• Convex curves moving homothetically by negative powers of their curvature
• Asymptotic shape of cusp singularities in curve shortening
• Optimal systems and invariant solutions for the curve shortening problem
• Contraction of convex hypersurfaces by their affine normal
• Nonhomogeneous Gauss Curvature Flows
• Classification of limiting shapes for isotropic curve flows

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