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VOL. 47.2 | 2007 Numerical study and examples on singularities of solutions to anisotropic crystalline curvature flows of nonconvex polygonal curves
Chiaki Hirota, Tetsuya Ishiwata, Shigetoshi Yazaki

Editor(s) Hideo Kozono, Takayoshi Ogawa, Kazunaga Tanaka, Yoshio Tsutsumi, Eiji Yanagida

Abstract

We construct explicit solutions of the anisotropic motion of closed polygonal plane curves by a power of crystalline cuvature, in the case where the initial curves are nonconvex and the power is less than one: The solutions develop degenerate pinching singularities of a "whisker"-type and a split-type in finite time, and do not become convex polygons. Moreover, in the splitting case, we conjecture degenerate pinching rate from numerical experiments.

Information

Published: 1 January 2007
First available in Project Euclid: 16 December 2018

zbMATH: 1143.35308
MathSciNet: MR2387254

Digital Object Identifier: 10.2969/aspm/04720543

Rights: Copyright © 2007 Mathematical Society of Japan

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