Abstract
We study the problem of uniqueness of complete noncompact spacelike hypersurfaces immersed in a generalized Robertson-Walker spacetime, which is supposed to satisfy the so-called null convergence condition. By extending a technique of S.T. Yau and imposing a suitable restriction on the norm of the gradient of the height function of the hypersurface, we obtain rigidity theorems in such ambient spacetimes. Furthermore, we also establish nonparametric results concerning entire vertical graphs.
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