Electronic Journal of Differential Equations (Mar 2018)
Solutions to the maximal spacelike hypersurface equation in generalized Robertson-Walker spacetimes
Abstract
We apply some generalized maximum principles for establishing uniqueness and nonexistence results concerning maximal spacelike hypersurfaces immersed in a generalized Robertson-Walker (GRW) spacetime, which is supposed to obey the so-called timelike convergence condition (TCC). As application, we study the uniqueness and nonexistence of entire solutions of a suitable maximal spacelike hypersurface equation in GRW spacetimes obeying the TCC.