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.

中文翻译：

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关于在 $${{\pmb {\mathbb {R}}}}^n\backslash \{0\}$$ R n \ { 0 } 和外部域上最大化超曲面的区域的评论

在本说明中，我们为具有孤立奇点的整个区域最大化超曲面提供了完整的分类。我们还构建了一个有趣的插图示例。对于在外部域上最大化超曲面的区域，我们获得了它们在无穷远处的渐近行为的部分结果。我们还建立了区域最大化超曲面的外部 Dirichlet 问题的可解性。