Splitting theorems for hypersurfaces in Lorentzian manifolds (Q1986038)

The author studies splitting theorems for hypersurfaces in Lorentzian manifolds. She discusses different comparison results, for example, the cosmological comparison condition, the Riccati comparison, the mean curvature comparison, etc. Maximality in the $\Sigma$ injectivity radius of manifold $(M,g,\Sigma)$ satisfying the cosmological comparison condition to the bounds on distance, area, volume by making use of curvature is studied. Further, the splitting result and existence of $\Sigma$ ray are obtained. Moreover, the author investigates the splitting theorem for maximal volume and introduces a function $\nu$ on the comparison space.