Gradient estimates for the constant mean curvature equation in hyperbolic space

Abstract

AbstractWe establish gradient estimates for solutions to the Dirichlet problem for the constant mean curvature equation in hyperbolic space. We obtain these estimates on bounded strictly convex domains by using the maximum principles theory of Φ-functions of Payne and Philippin. These estimates are then employed to solve the Dirichlet problem when the mean curvatureHsatisfiesH< 1 under suitable boundary conditions.