Communications in Analysis and Geometry

Volume 18 (2010)

Number 1

Contracting convex immersed closed plane curves with fast speed of curvature

Pages: 23 – 75

DOI: https://dx.doi.org/10.4310/CAG.2010.v18.n1.a2

Authors

Chi-Cheung Poon (Department of Mathematics, National Chung Cheng University, Taiwan)

Dong-Ho Tsai (Department of Mathematics, National Tsing Hua University, Taiwan)

Abstract

We study the contraction of a convex immersed plane curve along its normalvector direction with speed function $\frac{1}{\alpha}k^{\alpha}$, where$k>0$ is the curvature of the evolving curve and $\alpha>1$ is aconstant. We show that the blow-up rate of the curvature is always oftype one and the rescaled solution will converge to a limit that mayor may not be degenerate.

Published 1 January 2010