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Area-preserving evolution of nonsimple symmetric plane curves

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Abstract

The area-preserving nonlocal flow in the plane is investigated for locally convex closed curves, which may be nonsimple. For highly symmetric convex curves, the flows converge to m-fold circles, while for Abresch–Langer type curves, the convergence to m-fold circles happens if and only if the enclosed algebraic area is positive.

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Authors and Affiliations

  1. Department of Mathematics, Southeast University, Nanjing, 210096, People’s Republic of China

    Xiao-Liu Wang

  2. School of Science, Dalian Ocean University, No. 52 Heishijiao Street, Dalian, 116023, People’s Republic of China

    Ling-Hua Kong

Authors
  1. Xiao-Liu Wang
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  2. Ling-Hua Kong
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Correspondence to Xiao-Liu Wang.

Additional information

This work is partially supported by the National Natural Science Foundation of China 11101078, 11171064 and the Education Department Program of Liaoning Province L2010068.

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Wang, XL., Kong, LH. Area-preserving evolution of nonsimple symmetric plane curves. J. Evol. Equ. 14, 387–401 (2014). https://doi.org/10.1007/s00028-014-0219-5

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  • DOI: https://doi.org/10.1007/s00028-014-0219-5

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