Andrews, BenMcCoy, JamesWheeler, GlenWheeler, Valentina-Mira2023-02-281465-3060http://hdl.handle.net/1885/286527We use a gradient flow to deform closed planar curves to curves with least variation of geodesic curvature in the L2 sense. 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 multiply covered circle. Moreover, we show that curves in any homotopy class with initially small L3∥ks∥∥22 enjoy a uniform length bound under the flow, yielding the convergence result in these cases.application/pdfen-AU© 2020 The authorsconstant mean curvaturecurvature flowgeometric evolution equation202010.2140/gt.2020.24.10192021-12-26