Comparison Theorems in Lorentzian Geometry and applications to spacelike hypersurfaces
arXiv:1104.5612 · doi:10.1016/j.geomphys.2011.11.004
Abstract
In this paper we prove Hessian and Laplacian comparison theorems for the Lorentzian distance function in a spacetime with sectional (or Ricci) curvature bounded by a certain function by means of a comparison criterion for Riccati equations. Using these results, under suitable conditions, we are able to obtain some estimates on the higher order mean curvatures of spacelike hypersurfaces satisfying a Omori-Yau maximum principle for certain elliptic operators.
23 pages. Final version. To appear on Journal of Geometry and Physics