Self-shrinkers to the mean curvature flow asymptotic to isoparametric cones

Chang, Po-Yao; Spruck, Joel

doi:10.1090/tran/6957

Self-shrinkers to the mean curvature flow asymptotic to isoparametric cones
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by Po-Yao Chang and Joel Spruck PDF

Trans. Amer. Math. Soc. 369 (2017), 6565-6582 Request permission

Abstract:

In this paper we construct an end of a self-similar shrinking solution of the mean curvature flow asymptotic to an isoparametric cone $C$ and lying outside $C$. We call a cone $C$ in $\mathbb {R}^{n+1}$ an isoparametric cone if $C$ is the cone over a compact embedded isoparametric hypersurface $\Gamma \subset \mathbb {S}^n$. The theory of isoparametic hypersurfaces is extremely rich, and there are infinitely many distinct classes of examples, each with infinitely many members.

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