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Rigidity theorems in the hyperbolic space. (English) Zbl 1259.53056
Summary: As a suitable application of the well known generalized maximum principle of Omori-Yau, we obtain rigidity results concerning complete hypersurfaces immersed with bounded mean curvature in the (n+1)-dimensional hyperbolic space n+1 . In our approach, we explore the existence of a natural duality between n+1 and the half n+1 of the de Sitter space 𝕊 1 n+1 , which models the so-called steady state space.
MSC:
53C42Immersions (differential geometry)
53C50Lorentz manifolds, manifolds with indefinite metrics
53C24Rigidity results (differential geometry)