Evolution of closed curves by length-constrained curve diffusion

Authors

James A. McCoy, University of NewcastleFollow
Glen Wheeler, University of WollongongFollow
Yuhan Wu, University of WollongongFollow

RIS ID

139774

Publication Details

McCoy, J., Wheeler, G. & Wu, Y. (2019). Evolution of closed curves by length-constrained curve diffusion. Proceedings of the American Mathematical Society, 147 (8), 3493-3506.

Abstract

We show that any initial closed curve suitably close to a circle flows under length-constrained curve diffusion to a round circle in infinite time with exponential convergence. We provide an estimate on the total length of time for which such curves are not strictly convex. We further show that there are no closed translating solutions to the flow and that the only closed rotators are circles.

Grant Number

ARC/DP150100375