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High order curvature flows of plane curves with generalised Neumann boundary conditions

 Hold Date 2020-03-12 15:30～2020-03-12 17:00 Place 九州大学 伊都キャンパス ウエスト1号館 中セミナー室 W1-C-716 Object person Speaker James McCoyb (The University of Newcastle, Australia)
Abstract:
We consider the parabolic polyharmonic diffusion and $L^2$-gradient flows of the $m$-th arclength derivative of curvature for regular closed curves evolving with generalised Neumann boundary conditions. In the polyharmonic case, we prove that if the curvature of the initial curve is small in $L^2$, then the evolving curve converges exponentially in the $C^\infty$ topology to a straight horizontal line segment. The same behaviour is shown for the $L^2$-gradient flows provided the energy of the initial curve is sufficiently small. In each case the smallness conditions depend only on $m$.  This is joint work with Glen Wheeler and Yuhan Wu.