Non-convergence and instability in the asymptotic behaviour of curves evolving by curvature

DOI10.4310/CAG.2002.v10.n2.a8zbMath1029.53079OpenAlexW3146836907MaRDI QIDQ1866519

Ben Andrews

Publication date: 7 April 2003

Published in: Communications in Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4310/cag.2002.v10.n2.a8

zbMATH Keywords

curvatureconvex closed curvescurves motiondifferential equations asymptotics behaviour

Mathematics Subject Classification ID

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Classification of limiting shapes for isotropic curve flows ⋮ Flow by powers of the Gauss curvature ⋮ On flows that preserve parallel curves and their formation of singularities ⋮ The evolution of immersed locally convex plane curves driven by anisotropic curvature flow ⋮ Stochastic approximations to curve-shortening flows via particle systems ⋮ Convex hypersurfaces evolving by volume preserving curvature flows ⋮ Tracking the critical points of curves evolving under planar curvature flows ⋮ Ancient finite entropy flows by powers of curvature in \(\mathbb{R}^2\) ⋮ Contracting convex immersed closed plane curves with slow speed of curvature ⋮ Functional analytic properties and regularity of the Möbius-invariant Willmore flow in \(\mathbb{R}^n\) ⋮ Asymptotic closeness to limiting shapes for expanding embedded plane curves

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