Weak maximum principles and geometric estimates for spacelike hypersurfaces in generalized Robertson-Walker spacetimes. (English) Zbl 1328.53066
Summary: In this paper we deal with complete space-like hypersurfaces in a generalized Robertson-Walker space-time. Using as main analytical tool a new local form of the weak maximum principle for a class of operators including the Lorentzian mean curvature operator, we obtain some mean curvature estimates and height estimates for space-like graphs with nice Bernstein type consequences. We also give height estimates for space-like hypersurfaces with constant higher order mean curvature, which are obtained via the local form of the weak maximum principle recently given in [L. J. Alías et al., “A new open form of the weak maximum principle and geometric applications”, Commun. Anal. Geom. (to appear)] for a class of operators including those constructed from the Newton tensors of a hypersurface.
MSC:
| 53C40 | Global submanifolds |
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
| 53C50 | Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics |
Keywords:
generalized Robertson-Walker spacetimes; weak maximum principle; space-like graphs; Lorentzian mean curvature operatorReferences:
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