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The blow up analysis of the general curve shortening flow

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Abstract

It is shown that the curvature function satisfies a nonlinear evolution equation under the general curve shortening flow and a detailed asymptotic behavior of the closed curves is presented when they contract to a point in finite time.

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Authors and Affiliations

  1. School of Mathematical Sciences, Guangxi Normal University, Guilin, 541004, P. R. China

    Rong Li Huang

  2. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, P. R. China

    Rong Li Huang & Ji Guang Bao

Authors
  1. Rong Li Huang
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  2. Ji Guang Bao
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Correspondence to Rong Li Huang.

Additional information

Supported by National Natural Science Foundation of China (Grant No. 10671022) and Doctoral Programme Foundation of Institute of Higher Education of China (Grant No. 20060027023)

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Huang, R.L., Bao, J.G. The blow up analysis of the general curve shortening flow. Acta. Math. Sin.-English Ser. 27, 2107–2128 (2011). https://doi.org/10.1007/s10114-011-0126-4

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  • DOI: https://doi.org/10.1007/s10114-011-0126-4

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