Calculus of Variations and Geometric Measure Theory

A. Mramor - S. Wang

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

created by wang on 13 Nov 2020


Published Paper

Inserted: 13 nov 2020
Last Updated: 13 nov 2020

Journal: International Mathematics Research Notices
Volume: 2020
Pages: 1933–1941
Year: 2017

ArXiv: 1708.06581 PDF


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.