Height Estimates for Spacelike Hypersurfaces with Constant $k$-Mean Curvature in GRW Spacetimes

Abstract:

      In this paper, using the generalized Omori-Yau maximum principle, we obtain height estimates for spacelike hypersurface in a generalized Robertson-Walker (GRW) spacetime with constant higher order mean curvature and whose boundary is contained in a slice. Furthermore, we apply these results to draw some topological conclusions. Finally, considering the Omori-Yau maximum principle for the Laplacian and for more general elliptic trace type differential operators, we have some further non-existence results.