The Dirichlet problem for constant mean curvature surfaces in Heisenberg space

Al�as, Luis J.; Dajczer, Marcos; Rosenberg, Harold
December 2007
Calculus of Variations & Partial Differential Equations;Dec2007, Vol. 30 Issue 4, p513
Academic Journal
We study constant mean curvature graphs in the Riemannian three- dimensional Heisenberg spaces $${\mathcal{H} = \mathcal{H}(\tau)}$$ . Each such $${\mathcal{H}}$$ 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 $${\mathcal{H}}$$ with respect to the Riemannian submersion over certain domains $${\Omega \subset \mathbb{R}^2}$$ taking on prescribed boundary values.


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