Characterizations of Spacelike Hyperplanes in the Steady State Space via Generalized Maximum Principles

Abstract

We deal with complete spacelike hypersurfaces immersed in the half of the de Sitter space, which models the so-called steady state space. In this setting, under some appropriated constraints on the geometry of such a spacelike hypersurface, we apply suitable generalized maximum principles in order to guarantee that it must be isometric to the Euclidean space.