FOLIATIONS OF HYPERBOLIC SPACE BY CONSTANT MEAN CURVATURE HYPERSURFACES

ABSTRACT. We show that the constant mean curvature hypersurfaces in H n+1 spanning the boundary of a star shaped C 1,1 domain in S n ∞(H n+1) give a foliation of H n+1. We also show that if Γ is a closed codimension-1 C 2,α submanifold in S n ∞(H n+1) bounding a unique constant mean curvature hypersurface ΣH in H n+1 with ∂∞ΣH = Γ for any H ∈ (−1, 1), then the constant mean curvature hypersurfaces {ΣH} foliates H n+1. 1.