The Dirichlet problem for the constant mean curvature equation in Sol_3

Abstract

A version of the Jenkins-Serrin theorem for the existence of CMC graphs over bounded domains with infinite boundary data in Sol${}_3$ is proved. Moreover, we construct examples of admissible domains where the results may be applied.

Final version. Accepted for publication on Illinois Journal of Mathematics

References in corpus (1)

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