The Dirichlet Problem for constant mean curvature graphs in 𝕄 × ℝ

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.

A height estimate for constant mean curvature graphs and uniqueness

In this paper, we give a height estimate for constant mean curvature graphs. Using this result we prove two results of uniqueness for the Dirichlet problem associated to the constant mean curvature equation on unbounded domains. 2000 Mathematics Subject Classification. 53A10. Introduction The surfaces with constant mean curvature are the mathematical modelling of soap films. These surfaces appe...

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...