A Sixth Order Curvature Flow of Plane Curves with Boundary Conditions

  • James McCoyEmail author
  • Glen Wheeler
  • Yuhan Wu
Part of the MATRIX Book Series book series (MXBS, volume 2)


We show that small energy curves under a particular sixth order curvature flow with generalised Neumann boundary conditions between parallel lines converge exponentially in the C topology in infinite time to straight line segments.


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The research of the first and second authors was supported by Discovery Project grant DP150100375 of the Australian Research Council. The research was conducted while the first author was a staff member of the University of Wollongong. He completed part of this research at the MATRIX facilities in Cresswick and gratefully acknowledges their support. The research of the third author was supported by a University of Wollongong Faculty of Engineering and Information Sciences Postgraduate research scholarship.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of NewcastleCallaghanAustralia
  2. 2.University of WollongongWollongongAustralia

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