Uniqueness results for constant mean curvature graphs

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...

Some Characterization, Uniqueness and Existence Results for Euclidean Graphs of Constant Mean Curvature with Planar Boundary

We establish the existence and uniqueness of solutions to the Dirichlet problem for the cmc surface equation, including the minimal one, for zero boundary data, in certain domains of the plane. We obtain results that characterize the sphere and cmc graphs among compact embedded cmc surfaces with planar boundary satisfying certain geometric conditions. We also find conditions that imply that a c...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

A note on radial graphs with constant mean curvature

Let be a smooth domain on the unit sphere S whose closure is contained in an open hemisphere and denote by H the mean curvature of ∂ as a submanifold of with respect to the inward unit normal. It is proved that for each real number H that satisfies inf H > −H ≥ 0, there exists a unique radial graph on bounded by ∂ with constant mean curvature H . The orientation on the graph is based on the nor...