Geodesic
Embedded self-similar shrinkers of genus $0$
Simon Brendle1
1 Stanford University, Stanford, CA
Annals of mathematics, Tome 183 (2016) no. 2, pp. 715-728.

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We confirm a well-known conjecture that the round sphere is the only compact, embedded self-similar shrinking solution of mean curvature flow in $\mathbb{R}^3$ 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.
DOI : 10.4007/annals.2016.183.2.6

Simon Brendle 1

1 Stanford University, Stanford, CA 
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Simon Brendle. Embedded self-similar shrinkers of genus $0$. Annals of mathematics, Tome 183 (2016) no. 2, pp. 715-728. doi : 10.4007/annals.2016.183.2.6. http://geodesic.mathdoc.fr/articles/10.4007/annals.2016.183.2.6/

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