Length-constrained curve diffusion
Differential Geometry
2019-01-23 v1
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.
Cite
@article{arxiv.1901.07128,
title = {Length-constrained curve diffusion},
author = {James McCoy and Glen Wheeler and Yuhan Wu},
journal= {arXiv preprint arXiv:1901.07128},
year = {2019}
}
Comments
13 pages