Preprint A475/2006
The Dirichlet problem for CMC surfaces in Heisenberg space
Harold Rosenberg | AlĂ­as, Luis | Dajczer, Marcos
We study constant mean curvature graphs in the Riemannian 3-dimensional Heisenberg spaces $\He=\He(\tau)$. Each such $\He$ is the total space of a Riemannian submersion onto the Euclidean plane $\R^2$ with geodesic fibers the orbits of a Killing field. We prove the existence and uniqueness of CMC graphs in $\He$ with respect to the Riemannian submersion over certain domains $\Omega\subset\R^2$ taking on prescribed boundary values.