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Prescribed Mean Curvature Hypersurfaces in Hn+1(-1) with Convex Planar Boundary, I

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Abstract

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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Authors and Affiliations

  1. Departamento de Matemática, Campus do Pici, Universidade Federal do Ceará, 60455-760, Fortaleza-Ce, Brazil. e-mail

    J. Lucas M. Barbosa

  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

    Ricardo Sa Earp

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  1. J. Lucas M. Barbosa
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  2. Ricardo Sa Earp
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Barbosa, J.L.M., Sa Earp, R. Prescribed Mean Curvature Hypersurfaces in Hn+1(-1) with Convex Planar Boundary, I. Geometriae Dedicata 71, 61–74 (1998). https://doi.org/10.1023/A:1005046021921

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  • DOI: https://doi.org/10.1023/A:1005046021921

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