Abstract
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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L. J. Alías was partially supported by MEC/FEDER project MTM2004-04934-C04-02 and Fundación Séneca project 00625/PI/04, Spain.
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Alías, L.J., Dajczer, M. & Rosenberg, H. The Dirichlet problem for constant mean curvature surfaces in Heisenberg space. Calc. Var. 30, 513–522 (2007). https://doi.org/10.1007/s00526-007-0101-1
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DOI: https://doi.org/10.1007/s00526-007-0101-1