Foliations of Hyperbolic Space by Constant Mean Curvature Hypersurfaces
Abstract
We show that the constant mean curvature hypersurfaces in the hyperbolic n-space spanning the boundary of a star shaped C1,1 domain in the asymptotic sphere give a foliation of the hyperbolic n-space. We also show that if C is a closed codimension-1 C2,a submanifold in the asymptotic sphere bounding a unique constant mean curvature hypersurface SH in the hyperbolic n-space with asymptotic boundary C for any -1<H<1, then the constant mean curvature hypersurfaces SH foliates the hyperbolic n-space.
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