An unknottedness result for self shrinkers with multiple ends

Abstract

In this article we prove an unknottedness result for self shrinkers in ${\mathbb{R}}^3$ with multiple asymptotically conical ends which bound a handlebody in a natural sense, using the mean curvature flow. As a corollary of this and previous work, asymptotically conical self shrinkers with two ends are unknotted.

Revisited and majorly revised. Results and exposition improved, including some new arguments/details added. Comments welcome!

References in corpus (5)

• Mean curvature flow with surgery
• A Topological Property of Asymptotically Conical Self-Shrinkers of Small Entropy
• Asymptotic structure of self-shrinkers
• Self-shrinking Platonic solids
• Multiplicity one for min-max theory in compact manifolds with boundary and its applications