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The Shrinking Figure Eight and Other Solitons for the Curve Diffusion Flow

  • Maureen Edwards
  • Alexander Gerhardt-Bourke
  • James McCoyEmail author
  • Glen Wheeler
  • Valentina-Mira Wheeler
Chapter
  • 685 Downloads

Abstract

In this article we investigate the dynamics of special solutions to the surface diffusion flow of idealised ribbons. This reduces to studying the curve diffusion flow for the profile curve of the ribbon. We provide: (1) a complete classification of stationary solutions; (2) qualitative results on shrinkers, translators, and rotators; and (3) an explicit parametrisation of a shrinking figure eight curve.

Keywords

Curvature flow Curve diffusion Self-similar solution 

Mathematics Subject Classification (2010)

35J35 35K30 53C44 58J35 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Maureen Edwards
    • 1
  • Alexander Gerhardt-Bourke
    • 1
  • James McCoy
    • 1
    Email author
  • Glen Wheeler
    • 1
  • Valentina-Mira Wheeler
    • 1
  1. 1.University of WollongongWollongongAustralia

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