The Dirichlet problem for the constant mean curvature equation in Sol_3

TL;DR

This paper extends the Jenkins-Serrin theorem to solve the constant mean curvature equation in Sol_3, providing existence results for CMC graphs over certain domains with infinite boundary data.

Contribution

It proves a Jenkins-Serrin type theorem for CMC graphs in Sol_3 and constructs examples of admissible domains for these solutions.

Findings

Existence of CMC graphs over bounded domains with infinite boundary data in Sol_3.

Construction of admissible domains where the theorem applies.

Extension of classical results to the Sol_3 geometry.

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.