Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes
In Section 3, the relation between spacelike hypersurfaces and spacelike graphs in generalized Robertson-Walker spacetimes is given, and the conditions under which all these hypersurfaces are compact are studied. Section 4 contains two new integral formulas for compact spacelike hypersurfaces. In Section 5, a new technique to solve the problem: ``when is a complete spacelike hypersurface of constant mean curvature in a generalized Robertson-Walker spacetime totally umbilical and a slice?'' is introduced. Finally, the natural conditions \(f'' \leq 0\) and \(\text{Ric} > (n - 1) (ff'' - f'{}^2)\) are imposed to solve a Bernstein-type problem.
scientific article; zbMATH DE number 727347
scientific article