Prescribed Mean Curvature Hypersurfaces in Hn+1(-1) with Convex Planar Boundary, I
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We study immersed prescribed mean curvature compact hypersurfaces with boundary in Hn+1(-1). When the boundary is a convex planar smooth manifold with all principal curvatures greater than 1, we solve a nonparametric Dirichlet problem and use this, together with a general flux formula, to prove a parametric uniqueness result, in the class of all immersed compact hypersurfaces with the same boundary. We specialize this result to a constant mean curvature, obtaining a characterization of totally umbilic hypersurface caps.
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- Prescribed Mean Curvature Hypersurfaces in Hn+1(-1) with Convex Planar Boundary, I
Volume 71, Issue 1 , pp 61-74
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- mean curvature
- hyperbolic space
- Dirichlet problem.
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- 1. Departamento de Matemática, Campus do Pici, Universidade Federal do Ceará, 60455-760, Fortaleza-Ce, Brazil. e-mail
- 2. Departamento de Matemática, Pantifíca Universidad Católica do Rio de Janeiro, Rua Marques de São Vicente 225, 24, 453-900, Rio de Janeiro-RJ, Brazil. e-mail