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
Impera, D. (2012). Comparison theorems in Lorentzian geometry and applications to spacelike hypersurfaces. JOURNAL OF GEOMETRY AND PHYSICS, 62, 412-426 [10.1016/j.geomphys.2011.11.004].
Comparison theorems in Lorentzian geometry and applications to spacelike hypersurfaces
IMPERA, DEBORA
2012
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
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