Calculus of Variations and Partial Differential Equations

, Volume 34, Issue 2, pp 153–178

Expanding convex immersed closed plane curves


    • Department of MathematicsNational Taiwan University
  • Chi-Cheung Poon
    • Department of MathematicsNational Chung Cheng University
  • Dong-Ho Tsai
    • Department of MathematicsNational Tsing Hua University

DOI: 10.1007/s00526-008-0180-7

Cite this article as:
Lin, T., Poon, C. & Tsai, D. Calc. Var. (2009) 34: 153. doi:10.1007/s00526-008-0180-7


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)

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© Springer-Verlag 2008