Contracting convex immersed closed plane curves with slow speed of curvature

Yu Chu Lin, Chi Cheung Poon, Dong Ho Tsai

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The authors study the contraction of a convex immersed plane curve with speed 1/αk α, where α ∈ (0, 1] is a constant, and show that, if the blow-up rate of the curvature is of type one, it will converge to a homothetic self-similar solution. They also discuss a special symmetric case of type two blow-up and show that it converges to a translational self-similar solution. In the case of curve shortening flow (i.e., when α = 1), this translational self-similar solution is the familiar "Grim Reaper" (a terminology due to M. Grayson).

Original languageEnglish
Pages (from-to)5735-5763
Number of pages29
JournalTransactions of the American Mathematical Society
Volume364
Issue number11
DOIs
Publication statusPublished - 2012 Jul 26

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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