All solutions of the CMC-equation in $${\mathbb{H}^n\times\mathbb{R}}$$ invariant by parabolic screw motion

Abstract

In this paper, we give all solutions of the constant mean curvature equation in \({\mathbb{H}^n\times\mathbb{R}}\) that are invariant by parabolic screw motion and we give the full description of their geometric behaviors. Some of these solutions give examples of non-trivial entire stable horizontal graphs that are not vertical graphs.