The Dirichlet problem for constant mean curvature surfaces in Heisenberg space

Alias, Luis J.; Dajczer, Marcos; Rosenberg, Harold

The Dirichlet problem for constant mean curvature surfaces in Heisenberg space

Authors

Alias, Luis J.

Dajczer, Marcos

Rosenberg, Harold

Description

We study constant mean curvature graphs in the Riemannian 3-dimensional Heisenberg spaces ${\cal H}={\cal H}(τ)$. Each such ${\cal H}$ is the total space of a Riemannian submersion onto the Euclidean plane $\mathbb{R}^2$ with geodesic fibers the orbits of a Killing field. We prove the existence and uniqueness of CMC graphs in ${\cal H}$ with respect to the Riemannian submersion over certain domains $Ω\subset\mathbb{R}^2$ taking on prescribed boundary values.