SOME RIGIDITY RESULTS FOR SPATIALLY CLOSED SPACETIMES

1. Introduction. The geometric maximum principle for (smooth) hypersurfaces is a basic tool in Riemannian geometry. A corresponding maximum principle for spacelike hypersurfaces has become a useful tool in Lorentzian geometry, as well. These geometric maximum principles are consequences of the analytic maximum principle for second order linear elliptic PDE’s (see e.g., [GT]). More closely related to the considerations of thi