Expanding convex immersed closed plane curves

DOI10.1007/s00526-008-0180-7zbMath1177.35114OpenAlexW2156000367MaRDI QIDQ1006415

Dong-Ho Tsai, Chi-Cheung Poon, Tai-Chia Lin

Publication date: 24 March 2009

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-008-0180-7

zbMATH Keywords

singularitiesself-similar solutioncurvature blow-up rate

Mathematics Subject Classification ID

Related Items (10)

Deforming a hypersurface by Gauss curvature and support function ⋮ The evolution of immersed locally convex plane curves driven by anisotropic curvature flow ⋮ Application of Andrews and Green-Osher inequalities to nonlocal flow of convex plane curves ⋮ The stability of \(m\)-fold circles in the curve shortening problem ⋮ A structure-preserving parametric finite element method for area-conserved generalized curvature flow ⋮ On a nonlinear parabolic equation arising from anisotropic plane curve evolution ⋮ Blow-up rates for the general curve shortening flow ⋮ On length-preserving and area-preserving nonlocal flow of convex closed plane curves ⋮ Evolution of highly symmetric curves under the shrinking curvature flow ⋮ Contracting convex immersed closed plane curves with slow speed of curvature

Cites Work

• Unnamed Item
• Convergence, asymptotic periodicity, and finite-point blow-up in one- dimensional semilinear heat equations
• Geometric expansion of convex plane curves
• On the formation of singularities in the curve shortening flow
• The heat equation shrinking convex plane curves
• An expansion of convex hypersurfaces
• Convergence of solutions of one-dimensional semilinear parabolic equations
• Evolving convex curves
• Convergence for degenerate parabolic equations
• Convex curves moving homothetically by negative powers of their curvature
• Blowup behavior of an equation arising from plane-curves expansion.
• Behavior of the gradient for solutions of parabolic equations on the circle
• Contracting convex immersed closed plane curves with slow speed of curvature
• The zero set of a solution of a parabolic equation.
• On the blow-up set for u_t=du^m+u^m, m>1
• Classification of limiting shapes for isotropic curve flows
• Blowup and convergence of expanding immersed convex plane curves

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