Minimizing Constant Mean Curvature Hypersurfaces in Hyperbolic Space

Details Minimizing Constant Mean Curvature Hypersurfaces in Hyperbolic Space Minimizing Constant Mean Curvature Hypersurfaces in Hyperbolic Space

2005-08-17

arxiv.org/abs/math/0508336v1

Geom. Dedicata 118 (2006) 157-171.

Mathematics

Differential Geometry

16 pages

Scientific paper

We study the constant mean curvature (CMC) hypersurfaces in hyperbolic space whose asymptotic boundaries are closed codimension-1 submanifolds in sphere at infinity. We consider CMC hypersurfaces as generalizations of minimal hypersurfaces. We naturally generalize some notions of minimal hypersurfaces like being area minimizing, convex hull property, exchange roundoff trick to the CMC hypersurface context. We also give a generic uniqueness result for CMC hypersurfaces in hyperbolic space.

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