, Volume 71, Issue 1, pp 61-74

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.