The Dirichlet problem for the minimal surface equation, with possible infinite boundary data, over domains in a Riemannian surface
L. Mazet, M. M. Rodríguez, H. Rosenberg · Proceedings of the London Mathematical Society · 2010
In this paper, we study the existence and uniqueness of solutions to Jenkins–Serrin type problems on domains in a Riemannian surface: infinite boundary data are allowed. In the case of unbounded domains, the study is focused on the hyperbolic plane. A counterexample to uniqueness is given for entire minimal graphs over ℍ2.