Some uniqueness results for constant mean curvature graphs
نویسنده
چکیده
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.
منابع مشابه
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...
متن کاملSome 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...
متن کاملDeformations of constant mean curvature 1/2 surfaces in H × R with vertical ends at infinity
We study constant mean curvature 1/2 surfaces in H × R that admit a compactification of the mean curvature operator. We show that a particular family of complete entire graphs over H admits a structure of infinite dimensional manifold with local control on the behaviors at infinity. These graphs also appear to have a half-space property and we deduce a uniqueness result at infinity. Deforming n...
متن کاملExistence and Uniqueness of Constant Mean Curvature Foliation of Asymptotically Hyperbolic 3-manifolds
We prove existence and uniqueness of foliations by stable spheres with constant mean curvature for 3-manifolds which are asymptotic to Anti-de Sitter-Schwarzschild metrics with positive mass. These metrics arise naturally as spacelike timeslices for solutions of the Einstein equation with a negative cosmological constant.
متن کاملConformal Killing graphs with prescribed mean curvature
We prove the existence and uniqueness of graphs with prescribed mean curvature function in a large class of Riemannian manifolds which comprises spaces endowed with a conformal Killing vector field.
متن کامل