Comparison Theorems in Lorentzian Geometry and applications to spacelike hypersurfaces
Differential Geometry
2015-05-28 v2
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.
Keywords
Cite
@article{arxiv.1104.5612,
title = {Comparison Theorems in Lorentzian Geometry and applications to spacelike hypersurfaces},
author = {Debora Impera},
journal= {arXiv preprint arXiv:1104.5612},
year = {2015}
}
Comments
23 pages. Final version. To appear on Journal of Geometry and Physics