Evolution of highly symmetric curves under the shrinking curvature flow

DOI10.1002/mma.4262zbMath1377.53085OpenAlexW2560176473MaRDI QIDQ4977839

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Publication date: 17 August 2017

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.4262

zbMATH Keywords

symmetryconvergenceblow upcurve shortening

Mathematics Subject Classification ID

Initial value problems for second-order parabolic equations (35K15)

Related Items (2)

On the isoperimetric inequality and surface diffusion flow for multiply winding curves ⋮ Evolving compact locally convex curves and convex hypersurfaces

Cites Work

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• On the saddle point property of Abresch-Langer curves under the curve shortening flow
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• The stability of \(m\)-fold circles in the curve shortening problem
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• On a simple maximum principle technique applied to equations on the circle
• Expanding convex immersed closed plane curves
• 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
• Evolving convex curves
• Convex curves moving homothetically by negative powers of their curvature
• Geometric curve evolution and image processing
• On the stability of \(m\)-fold circles and the dynamics of generalized curve shortening flows
• Contracting convex immersed closed plane curves with slow speed of curvature
• A stable manifold theorem for the curve shortening equation
• Classification of limiting shapes for isotropic curve flows
• A note on the Abresch—Langer conjecture

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