A Condition Ensuring Spatial Curves Develop Type-II Singularities Under Curve Shortening Flow
Differential Geometry
2015-12-17 v3
Abstract
We provide a condition for spatial curves which rules out the development of a type I singularity. The condition is that after the last time for which an inflection point develops, if the torsion is ever everywhere non-negative, the curve cannot develop a type I singularity.
Keywords
Cite
@article{arxiv.1209.4072,
title = {A Condition Ensuring Spatial Curves Develop Type-II Singularities Under Curve Shortening Flow},
author = {Gabriel Khan},
journal= {arXiv preprint arXiv:1209.4072},
year = {2015}
}
Comments
This draft replaces the second one, in which we fix some typos. The second draft replaced the first one, which contained a mistake in the calculations, reducing the generality of the theorem. Thank you to Ben Andrews for pointing this out