Foliations of Hyperbolic Space by Constant Mean Curvature Hypersurfaces

Details Foliations of Hyperbolic Space by Constant Mean Curvature Hypersurfaces Foliations of Hyperbolic Space by Constant Mean Curvature Hypersurfaces

2009-09-30

arxiv.org/abs/0909.5601v2

IMRN (2010) 1417-1431.

Mathematics

Differential Geometry

Scientific paper

10.1093/imrn/rnp175

We show that the constant mean curvature hypersurfaces in the hyperbolic n-space spanning the boundary of a star shaped C^{1,1} domain in the asymptotic sphere give a foliation of the hyperbolic n-space. We also show that if C is a closed codimension-1 C^{2,a} submanifold in the asymptotic sphere bounding a unique constant mean curvature hypersurface S_H in the hyperbolic n-space with asymptotic boundary C for any -1

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