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<H<1, then the constant mean curvature hypersurfaces { S_H} foliates the hyperbolic n-space.
Categories: math.DG math.GT