Geometriae Dedicata

, Volume 71, Issue 1, pp 61–74

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

  • J. Lucas M. Barbosa
  • Ricardo Sa Earp

DOI: 10.1023/A:1005046021921

Cite this article as:
Barbosa, J.L.M. & Sa Earp, R. Geometriae Dedicata (1998) 71: 61. doi:10.1023/A:1005046021921


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.

mean curvature hyperbolic space Dirichlet problem. 

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • J. Lucas M. Barbosa
    • 1
  • Ricardo Sa Earp
    • 2
  1. 1.Departamento de Matemática, Campus do PiciUniversidade Federal do CearáFortaleza-CeBrazil. e-mail
  2. 2.Departamento de MatemáticaPantifíca Universidad Católica do Rio de JaneiroRio de Janeiro-RJBrazil. e-mail

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