Remarks on area maximizing hypersurfaces over $\mathbb{R}^n\backslash\{0\}$ and exterior domains

Guanghao Hong

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arXiv · 1903.00789

Remarks on area maximizing hypersurfaces over $\mathbb{R}^n\backslash\{0\}$ and exterior domains

Guanghao Hong

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Abstract

In this note, we provide a complete classification for entire area maximizing hypersurfaces having an isolated singularity. We also construct an interesting illustrated example. For area maximizing hypersurfaces over exterior domains, we obtain a partial result on their asymptotic behavior at infinity. We also establish the solvability of exterior Dirichlet problems for area maximizing hypersurfaces.

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Guanghao Hong. 2019-03-02. Remarks on area maximizing hypersurfaces over $\mathbb{R}^n\backslash\{0\}$ and exterior domains. https://arxiv.org/abs/1903.00789

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