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

Alexander Mramor; Shengwen Wang

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arXiv · 1708.06581

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

Alexander Mramor·Shengwen Wang

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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.

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Alexander Mramor, Shengwen Wang. 2017-08-22. On the topological rigidity of self shrinkers in $\mathbb{R}^3$. https://arxiv.org/abs/1708.06581

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