The shrinking figure eight and other solitons for the curve diffusion flow
Differential Geometry
2015-05-13 v1
Abstract
In this article we investigate the dynamics of special solutions to the surface diffusion flow of idealised ribbons. This equation reduces to studying the curve diffusion flow for the profile curve of the ribbon. We provide: (1) a complete classification of stationary solutions; (2) qualitative results on shrinkers, translators, and rotators; and (3) an explicit parametrisation of a shrinking figure eight curve.
Keywords
Cite
@article{arxiv.1505.02978,
title = {The shrinking figure eight and other solitons for the curve diffusion flow},
author = {Maureen Edwards and Alexander Gerhardt-Bourke and James McCoy and Glen Wheeler and Valentina-Mira Wheeler},
journal= {arXiv preprint arXiv:1505.02978},
year = {2015}
}
Comments
18 pages, 2 figures