English

Gradient estimates for the constant mean curvature equation in hyperbolic space

Differential Geometry 2019-12-18 v1

Abstract

We 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\Phi-functions of Payne and Philippin. These estimates are then employed to solve the Dirichlet problem when the mean curvature HH satisfies H<1H<1 under suitable boundary conditions.

Keywords

Cite

@article{arxiv.1912.07864,
  title  = {Gradient estimates for the constant mean curvature equation in hyperbolic space},
  author = {Rafael López},
  journal= {arXiv preprint arXiv:1912.07864},
  year   = {2019}
}
R2 v1 2026-06-23T12:48:08.168Z