The stability of \(m\)-fold circles in the curve shortening problem

DOI10.1007/S00229-010-0410-0zbMath1209.53055OpenAlexW1980541194MaRDI QIDQ625507

Xiao-Liu Wang

Publication date: 17 February 2011

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-010-0410-0

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Stability in context of PDEs (35B35) Curves in Euclidean and related spaces (53A04)

Related Items (6)

On the isoperimetric inequality and surface diffusion flow for multiply winding curves ⋮ On a planar area-preserving curvature flow ⋮ Area-preserving evolution of nonsimple symmetric plane curves ⋮ Length-preserving evolution of non-simple symmetric plane curves ⋮ Evolution of highly symmetric curves under the shrinking curvature flow ⋮ Stability of geometric flows on the circle

Cites Work

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• On the saddle point property of Abresch-Langer curves under the curve shortening flow
• On the formation of singularities in the curve shortening flow
• Expanding convex immersed closed plane curves
• The normalized curve shortening flow and homothetic solutions
• The heat equation shrinking convex plane curves
• Geometric theory of semilinear parabolic equations
• Evolving convex curves
• A stable manifold theorem for the curve shortening equation
• Classification of limiting shapes for isotropic curve flows

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