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Self-similar solutions for the anisotropic affine curve shortening problem

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Abstract.

Similarity between the roles of the group \(SL(2,\bf R)\) on the equation for self-similar solutions of the anisotropic affine curve shortening problem and of the conformal group of \(S^2\) on the Nirenberg problem for prescribed scalar curvature is explored. Sufficient conditions for the existence of affine self-similar curves are established.

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Authors and Affiliations

  1. Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, , , , , , HK

    Jun Ai, Kai-Seng Chou & Juncheng Wei

Authors
  1. Jun Ai
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  2. Kai-Seng Chou
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  3. Juncheng Wei
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Additional information

Received June 26, 1999 / Accepted January 28, 2000 / Published online December 8, 2000

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Ai, J., Chou, KS. & Wei, J. Self-similar solutions for the anisotropic affine curve shortening problem. Calc Var 13, 311–337 (2001). https://doi.org/10.1007/s005260000075

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  • DOI: https://doi.org/10.1007/s005260000075

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