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

## TL;DR

This paper classifies entire area maximizing hypersurfaces with isolated singularities, constructs examples, and studies their behavior over exterior domains, including solving related Dirichlet problems.

## Contribution

Provides a complete classification of hypersurfaces with isolated singularities and advances understanding of their asymptotic behavior and boundary value problems.

## Key findings

- Complete classification of hypersurfaces with isolated singularities.
- Construction of illustrative examples.
- Partial results on asymptotic behavior at infinity and solvability of Dirichlet problems.

## 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.