Complete Constant Mean Curvature Spacelike Hypersurfaces in the Einstein-De Sitter Spacetime

The uniqueness and nonexistence results on complete constant mean curvature spacelike hypersurfaces lying between two spacelike slices in the Einstein–de Sitter spacetime are given. They are obtained from a Liouville-type theorem applied to a distinguished smooth function on a complete constant mean curvature hypersurface.