The Dirichlet problem for the minimal surface equation -with possible infinite boundary data- over domains in a Riemannian surface

TL;DR

This paper investigates the existence and uniqueness of solutions to the minimal surface Dirichlet problem with possibly infinite boundary data on domains in Riemannian surfaces, especially focusing on unbounded domains in the hyperbolic plane.

Contribution

It extends the theory of minimal surface equations to include unbounded domains with infinite boundary data in Riemannian surfaces, particularly in the hyperbolic plane.

Findings

Established conditions for existence and uniqueness of solutions.

Analyzed the problem in the context of unbounded domains in the hyperbolic plane.

Provided new insights into boundary value problems for minimal surfaces.

Abstract

In this paper, we study existence and uniqueness of solutions to Jenkins-Serrin type problems on domains in a Riemannian surface. In the case of unbounded domains, the study is focused on the hyperbolic plane.