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- Title
Space-like hypersurfaces with positive constant r -mean curvature in Lorentzian product spaces.
- Authors
A. Colares; Henrique de Lima
- Abstract
Abstract 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 $${-\mathbb{R} \times M^n}$$ , 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.
- Subjects
CURVES; GEOMETRY; DIFFERENTIAL geometry; ENUMERATIVE geometry
- Publication
General Relativity & Gravitation, 2008, Vol 40, Issue 10, p2131
- ISSN
0001-7701
- Publication type
Article
- DOI
10.1007/s10714-008-0621-9