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

By Laurent Mazet, M. M. Rodŕıguez, H. Rosenberg. 2008

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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.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/78bfd7485ff46dab128ad28be384ffacd690955a