Closed ideal planar curves
Ben Andrews, James McCoy, Glen Wheeler, Valentina‐Mira Wheeler
Abstract
2020, Mathematical Sciences Publishers. All rights reserved. We 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 L3kks k22 enjoy a uniform length bound under the flow, yielding the convergence result in these cases.
Topics & Concepts
MathematicsFlow (mathematics)Ideal (ethics)GeodesicPlanarHomotopyCurvatureMathematical analysisBounded functionGeometryPure mathematicsPhilosophyEpistemologyComputer graphics (images)Computer scienceGeometric Analysis and Curvature FlowsGeometry and complex manifoldsAdvanced Neuroimaging Techniques and Applications