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 C1,1 domain in S∞n(Hn+1) give a foliation of Hn+1. We also show that if Γ is a closed codimension-1 C2,α submanifold in S∞n(Hn+1) bounding a unique constant mean curvature hypersurface ΣH in Hn+1 with ∂∞ΣH = Γ for any H ∈ (−1,1), then the constant mean curvature hypersurfaces {ΣH} foliate Hn+1. [ABSTRACT FROM PUBLISHER]