Calculus of Variations and Partial Differential Equations

, Volume 34, Issue 2, pp 153-178

First online:

Expanding convex immersed closed plane curves

  • Tai-Chia LinAffiliated withDepartment of Mathematics, National Taiwan University Email author 
  • , Chi-Cheung PoonAffiliated withDepartment of Mathematics, National Chung Cheng University
  • , Dong-Ho TsaiAffiliated withDepartment of Mathematics, National Tsing Hua University

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We study the evolution driven by curvature of a given convex immersed closed plane curve. We show that it will converge to a self-similar solution eventually. This self-similar solution may or may not contain singularities. In case it does, we also have estimate on the curvature blow-up rate.

Mathematics Subject Classification (2000)

35K15 35K55