The Dirichlet problem for constant mean curvature surfaces in Heisenberg space

Details The Dirichlet problem for constant mean curvature surfaces in Heisenberg space The Dirichlet problem for constant mean curvature surfaces in Heisenberg space

2006-12-22

arxiv.org/abs/math/0612712v1

Calculus of Variations and PDE 30 (2007), 513--522

Mathematics

Differential Geometry

Scientific paper

10.1007/s00526-007-0101-1

We study constant mean curvature graphs in the Riemannian 3-dimensional Heisenberg spaces ${\cal H}={\cal H}(\tau)$. 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 $\Omega\subset\mathbb{R}^2$ taking on prescribed boundary values.

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