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

Abstract

In this paper, we obtain height estimates for spacelike hypersurfaces Σn of constant k-mean curvature, 1⩽k⩽n, in a generalized Robertson–Walker spacetime −I×ρPn and with boundary contained in a slice {s}×Pn. 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.