Mathematics – Logic
Scientific paper
Oct 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008gregr..40.2131c&link_type=abstract
General Relativity and Gravitation, Volume 40, Issue 10, pp.2131-2147
Mathematics
Logic
Lorentzian Products Spaces, Space-Like Hypersurfaces, Higher Order Mean Curvatures, Height Estimates
Scientific paper
In this paper we obtain a height estimate concerning compact space-like hypersurfaces Σ n immersed with some positive constant r-mean curvature into an ( n + 1)-dimensional Lorentzian product space {-mathbb{R} × M^n} , and whose boundary is contained into a slice { t} × M n . By considering the hyperbolic caps of the Lorentz Minkowski space {mathbb{L}^{n+1}} , we show that our estimate is sharp. Furthermore, we apply this estimate to study the complete space-like hypersurfaces immersed with some positive constant r-mean curvature into a Lorentzian product space. For instance, when the ambient space time is spatially closed, we show that such hypersurfaces must satisfy the topological property of having more than one end which constitutes a necessary condition for their existence.
Colares Gervasio A.
de Lima Henrique F.
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