Height estimates and half-space theorems for spacelike hypersurfaces in generalized Robertson-Walker spacetimes

In this paper, we obtain height estimates for spacelike hypersurfaces of constant k-mean curvature in a generalized Robertson–Walker spacetime and with boundary contained in a slice. As an application, we obtain some information on the topology at infinity of complete spacelike hypersurfaces of constant k-mean curvature properly immersed in a spatially closed generalized Robertson–Walker spacetime. Finally, using a version of the Omori–Yau maximum principle for the Laplacian and for more general elliptic trace-type differential operators, some non-existence results are also obtained