# Maximal hypersurfaces over exterior domains

## TL;DR

This paper investigates the exterior problem for the maximal surface equation, establishing the asymptotic behavior at infinity and proving unique solvability under certain boundary and asymptotic conditions.

## Contribution

It provides a detailed analysis of the exterior maximal surface problem, including asymptotics and uniqueness results, which were not previously fully understood.

## Key findings

- Precise asymptotic behavior of solutions at infinity.
- Unique solvability of the exterior Dirichlet problem.
- Conditions for admissible boundary data and prescribed asymptotics.

## Abstract

In this paper, we study the exterior problem for the maximal surface equation. We obtain the precise asymptotic behavior of the exterior solution at infinity. And we prove that the exterior Dirichlet problem is uniquely solvable given admissible boundary data and prescribed asymptotic behavior at infinity.