  We study the constant mean curvature (CMC) hypersurfaces in hyperbolic space
whose asymptotic boundaries are closed codimension-1 submanifolds in sphere at
infinity. We consider CMC hypersurfaces as generalizations of minimal
hypersurfaces. We naturally generalize some notions of minimal hypersurfaces
like being area minimizing, convex hull property, exchange roundoff trick to
the CMC hypersurface context. We also give a generic uniqueness result for CMC
hypersurfaces in hyperbolic space.
