%0 Journal Article
%T Embedded self-similar shrinkers of genus 0
%A S. Brendle
%J Mathematics
%D 2014
%I arXiv
%X We confirm a well-known conjecture that the round sphere is the only compact, embedded self-similar shrinking solution to the mean curvature flow with genus $0$. More generally, we show that the only properly embedded self-similar shrinkers in $\mathbb{R}^3$ with vanishing intersection form are the sphere, the cylinder, and the plane. This answers two questions posed by T. Ilmanen.
%U http://arxiv.org/abs/1411.4640v3