An unknottedness result for self shrinkers with multiple ends

2020/11/18 by Alexander Mramor, Mramor, Alexander
Mathematics · #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2011.09373

Abstract

In this article we prove an unknottedness result for self shrinkers in ℝ³ 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.

Citations

• On the Fundamental Group of a Compact Minimal Submanifold
• The unknottedness of minimal embeddings

Related

• An unknottedness result for noncompact self shrinkers
• Asymptotic structure of self-shrinkers
• Self-shrinkers whose asymptotic cones fatten
• Classification and rigidity of self-shrinkers in the Mean curvature flow
• Smooth compactness of self-shrinkers