A Condition Ensuring Spatial Curves Develop Type-II Singularities Under Curve Shortening Flow

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.

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

References in corpus (1)

• Distance comparison principle and Grayson type theorem in the three dimensional curve shortening flow

Cited by in corpus (2)

• Long-term behavior of curve shortening flow in ${\mathbb{R}}^3$
• Curvature-Torsion Entropy for Twisted Curves under Curve Shortening Flow