An unknottedness result for self shrinkers with multiple ends

TL;DR

This paper proves that certain self-shrinking surfaces in three-dimensional space with multiple ends are topologically unknotted, using mean curvature flow techniques, with implications for the classification of these surfaces.

Contribution

It establishes an unknottedness theorem for self shrinkers with multiple ends, extending previous results to a broader class of surfaces in geometric analysis.

Findings

Self shrinkers with multiple ends bound unknotted handlebodies.

Asymptotically conical self shrinkers with two ends are unknotted.

Uses mean curvature flow to prove topological properties.

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.