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Minimal hypersurfaces asymptotic to Simons cones
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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 $\sqrt{\frac pn}\mathbb{S}^p\times \sqrt{\frac{n-p}n} \mathbb{S}^{n-p}$ of $\mathbb{S}^{n+1}$
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Ancient mean curvature flow asymptotic to Simons cone
Ancient mean curvature flows asymptotic to the Simons cone from one side have unique asymptotics; adding mean convexity forces them to be stationary Hardt-Simon leaves.
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