On the Topological Rigidity of Compact Self-shrinkers in ℝ3-Reference-Cited by-同舟云学术

On the Topological Rigidity of Compact Self-shrinkers in ℝ3

Published:2018-04-17 Issue:7 Volume:2020 Page:1933-1941
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Mramor Alexander¹,Wang Shengwen²

Affiliation:

1. Department of Mathematics, University of California Irvine, Irvine, CA

2. Department of Mathematics, Johns Hopkins University, Baltimore, MD

Abstract

Abstract In this note we show that 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.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2020/7/1933/33136738/rny050.pdf

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