On the topological rigidity of self shrinkers in ${\mathbb{R}}^3$

Abstract

In this note we show that compact self shrinkers in ${\mathbb{R}}^3$ are "topologically standard" in that any genus $g$ compact self shrinker is ambiently isotopic to the standard genus $g$ embedded surface in ${\mathbb{R}}^3$. As a consequence self shrinking tori are unknotted.

arXiv comment8 pages, all comments welcome

References in corpus (2)

• Self-shrinking Platonic solids
• Closed Mean Curvature Self-Shrinking Surfaces of Generalized Rotational Type