An unknottedness result for noncompact self shrinkers

TL;DR

This paper extends an unknottedness theorem from compact to certain noncompact self shrinkers in mean curvature flow, specifically those with one asymptotically conical end, advancing understanding of their topology.

Contribution

It generalizes the unknottedness theorem to noncompact self shrinkers with a single asymptotically conical end, a class conjectured to include all finite topology, one-ended self shrinkers.

Findings

Extended unknottedness theorem to noncompact cases

Identified class of self shrinkers with one asymptotically conical end

Used mean curvature flow in the proof

Abstract

In this article we extend an unknottedness theorem for compact self shrinkers to the mean curvature flow to shrinkers with one asymptotically conical end, which conjecturally comprises the entire set of self shrinkers with finite topology and one end. The mean curvature flow itself is used in the argument presented.