 CARMA SEMINAR
 Speaker: Assoc. Prof. James McCoy, School of Mathematical and Physical Sciences, The University of Newcastle
 Title: The ideal curve flow of closed curves in the plane
 Location: Room V107, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 11:00 am, Fri, 9^{th} Aug 2019
 Abstract:
We consider an L2gradient flow of closed planar curves whose corresponding evolution equations is sixth order. Given a smooth initial curve we show that the solution to the flow exists for all time and, provided the length of the evolving curve remains bounded, smoothly converges to a multiplycovered circle. Moreover, we show that curves in any homotopy class with initially small L3‖ks‖2 enjoy a uniform length bound under the flow, yielding the convergence result in these cases. We also give some partial results for figure8 type solutions to the flow. This is joint work with Ben Andrews, Glen Wheeler and ValentinaMira Wheeler.
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