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Gradient estimates for the constant mean curvature equation in hyperbolic space
Published online by Cambridge University Press: 09 December 2019
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-functions of Payne and Philippin. These estimates are then employed to solve the Dirichlet problem when the mean curvature H satisfies H < 1 under suitable boundary conditions.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 6 , December 2020 , pp. 3216 - 3230
- Copyright
- Copyright © 2019 The Royal Society of Edinburgh
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