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

preprint2015arXivOpen access

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.

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