Abstract
We use the half-space model for the open set of a de Sitter space associated to the steady state space to obtain some sharp a priori estimates for the height and the slope of certain constant mean curvature spacelike graphs. These estimates allow us to prove some existence and uniqueness theorems about complete non-compact constant mean curvature spacelike hypersurfaces in de Sitter spaces with prescribed asymptotic future boundary. Their geometric properties are studied.
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