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

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.

8 pages