Comparison theorems in Lorentzian geometry and applications to spacelike hypersurfaces |
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Authors: | Debora Impera |
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Institution: | Dipartimento di Matematica, Università degli studi di Milano, via Saldini 50, I-20133 Milano, Italy |
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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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Keywords: | Comparison theorems Lorentzian geometry Higher order mean curvatures |
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