Comparison theorems in Lorentzian geometry and applications to spacelike hypersurfaces

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...

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Bibliographic Details
Published inJournal of geometry and physics Vol. 62; no. 2; pp. 412 - 426
Main Author Impera, Debora
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.02.2012
Subjects
Comparison theorems
Higher order mean curvatures
Lorentzian geometry
Higher order mean curvatures
Lorentzian geometry
Comparison theorems
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Summary: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.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2011.11.004