Foliations of Hyperbolic Space by Constant Mean Curvature Hypersurfaces

We show that the constant mean curvature hypersurfaces in Hn+1 spanning the boundary of a star-shaped C-1,C-1 domain in S-infinity(n)(Hn+1) give a foliation of Hn+1. We also show that if Gamma is a closed codimension-1 C-2,C-alpha submanifold in S-infinity(n)(Hn+1) bounding a unique constant mean curvature hypersurface Sigma(H) in Hn+1 with partial derivative(infinity)Sigma(H) = Gamma for any H is an element of (-1,1), then the constant mean curvature hypersurfaces {Sigma(H)} foliate Hn+1.