Minimal hypersurfaces asymptotic to Simons cones

Abstract

In this paper, we prove that, up to similarity, there are only two minimal hypersurfaces in ${\mathbb{R}}^{n+2}$ that are asymptotic to a Simons cone, i.e. the minimal cone over the minimal hypersurface $\sqrt{\frac{p}{n}}{\mathbb{S}}^p\times \sqrt{\frac{n-p}{n}}{\mathbb{S}}^{n-p}$ of ${\mathbb{S}}^{n+1}$

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