Comparison Theorems in Lorentzian Geometry and applications to spacelike hypersurfaces

Details Comparison Theorems in Lorentzian Geometry and applications to spacelike hypersurfaces Comparison Theorems in Lorentzian Geometry and applications to spacelike hypersurfaces

2011-04-29

arxiv.org/abs/1104.5612v2

Mathematics

Differential Geometry

23 pages. Final version. To appear on Journal of Geometry and Physics

Scientific paper

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.

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