Gradient estimates for the constant mean curvature equation in hyperbolic space

Gradient estimates for the constant mean curvature equation in hyperbolic space

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 emp...

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Veröffentlicht in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2020-12, Vol.150 (6), p.3216-3230
1. Verfasser: López, Rafael
Format: Artikel
Sprache:eng
Schlagworte:
Boundary conditions
Curvature
Dirichlet problem
Estimates
Mathematical analysis
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Zusammenfassung: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.
ISSN:0308-2105
1473-7124
DOI:10.1017/prm.2019.71