Normal geodesic graphs of constant mean curvature

Graphs of Constant Mean Curvature in Hyperbolic Space

We study the problem of finding constant mean curvature graphs over a domain of a totally geodesic hyperplane and an equidistant hypersurface Q of hyperbolic space. We find the existence of graphs of constant mean curvature H over mean convex domains ⊂ Q and with boundary ∂ for −H∂ < H ≤ |h|, where H∂ > 0 is the mean curvature of the boundary ∂ . Here h is the mean curvature respectively of the...

Existence of constant mean curvature graphs in hyperbolic space

We give an existence result for constant mean curvature graphs in hyperbolic space Hn+1. Let Ω be a compact domain of a horosphere in Hn+1 whose boundary ∂Ω is mean convex, that is, its mean curvature H∂Ω (as a submanifold of the horosphere) is positive with respect to the inner orientation. If H is a number such that −H∂Ω < H < 1, then there exists a graph over Ω with constant mean curvature H...

Constant Mean Curvature Graphs in a Strip of R

where H is a given nonzero number and φ is a smooth function on ∂Ω. The graph of a solution u ∈ C2(Ω) ∩ C0(Ω) is a surface with constant mean curvature H spanning the space curve given by the graph of φ. The orientation of this graph is given by N = (∇u,−1)/√1 + |∇u|2, that is, N points downward. From the physical viewpoint, a soap film in equilibrium between two regions of different gas pressu...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Some uniqueness results for constant mean curvature graphs

The aim of this paper is to give two uniqueness results for the Dirichlet problem associated to the constant mean curvature equation. We study constant mean curvature graphs over strips of R. The proofs are based on height estimates and the study of the asymptotic behaviour of solutions to the Dirichlet problem. 2000 Mathematics Subject Classification. 53A10.