On the Gauss map of complete spacelike hypersurfaces with bounded mean curvature in the Minkowski space (Q642869)

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scientific article; zbMATH DE number 5964516
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On the Gauss map of complete spacelike hypersurfaces with bounded mean curvature in the Minkowski space
scientific article; zbMATH DE number 5964516

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    On the Gauss map of complete spacelike hypersurfaces with bounded mean curvature in the Minkowski space (English)
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    27 October 2011
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    The paper deals with a complete space-like hypersurface \(\Sigma^{n}\subset \mathbb{L}^{n+1}\) bounded away from the past infinite of the Minkowski space \(\mathbb{L}^{n+1}\) with bounded mean curvature \(H>0\). The author shows that if the hyperbolic image of the \(n\)-dimensional connected manifold \(\Sigma^{n}\) is contained in the closure of a geodesic ball of centre \(e_{n+1}\in\mathbb{H}^{n}\), where \(\mathbb{H}^{n}\) is the \(n\)-dimensional hyperbolic space the radius \(\rho\) of which satisfies \[ \cosh \rho\leq 1 + \inf_{\Sigma}H, \] then \(\Sigma^{n}\) is a space-like hyperplane.
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    Gauss map
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    space-like hypersurface
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    Minkowski space
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