Selfsimilar shrinking curves for anisotropic curvature flow equations

DOI10.3792/pjaa.70.252zbMath0815.34026OpenAlexW2057083041MaRDI QIDQ1344806

Yoshikazu Giga, Claus Dohmen

Publication date: 27 June 1995

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.70.252

zbMATH Keywords

periodic solutionsecond order differential equationselfsimilar solutions of anisotropic curvature flow equations

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Non-Euclidean differential geometry (53A35)

Related Items (18)

Multiple solutions of the planar \(L_p\) dual Minkowski problem ⋮ On the planar dual Minkowski problem ⋮ Multiple solutions of the \(L_{p}\)-Minkowski problem ⋮ Existence of selfsimilar shrinking curves for anisotropic curvature flow equations ⋮ Motion by crystalline-like mean curvature: A survey ⋮ Variational analysis of the planar \(L_p\) dual Minkowski problem ⋮ Anisotropic area-preserving nonlocal flow for closed convex plane curves ⋮ An anisotropic area-preserving flow for convex plane curves ⋮ On the number of solutions to the discrete two-dimensional \(L_{0}\)-Minkowski problem. ⋮ \(2\pi\)-periodic self-similar solutions for the anisotropic affine curve shortening problem. II ⋮ 2\(\pi\)-periodic self-similar solutions for the anisotropic affine curve shortening problem ⋮ Existence of self-similar evolution of crystals grown from supersaturated vapor ⋮ Non-uniqueness of self-similar shrinking curves for an anisotropic curvature flow ⋮ On the planar \(L_p\)-Minkowski problem ⋮ Variational characterization for the planar dual Minkowski problem ⋮ On the planar $L_p$ Minkowski problem with sign-changing data ⋮ Crystalline flow starting from a general polygon ⋮ Nonuniqueness of solutions to the \(L_p\)-Minkowski problem

Cites Work

• Unnamed Item
• An isoperimetric inequality with applications to curve shortening
• Curve shortening makes convex curves circular
• The heat equation shrinking convex plane curves
• The heat equation shrinks embedded plane curves to round points
• Wulff theorem and best constant in Sobolev inequality
• Motion of a set by the curvature of its boundary
• Evolving plane curves by curvature in relative geometries
• Evolving plane curves by curvature in relative geometries. II
• Existence of selfsimilar shrinking curves for anisotropic curvature flow equations
• Existence of Periodic Solutions for Equations of Evolving Curves
• Convex Analysis

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