Rigidity and nonexistence of complete spacelike hypersurfaces in the steady state space
Differential Geometry
2025-01-22 v1
Abstract
We study complete spacelike hypersurfaces immersed in an open region of the de Sitter space which is known as the steady state space . In this setting, under suitable constraints on the behavior of the higher order mean curvatures of these hypersurfaces, we prove that they must be spacelike hyperplanes of . Nonexistence results concerning these spacelike hypersurfaces are also given. Our approach is based on a suitable extension of the Omori-Yau's generalized maximum principle due to Al\'{\i}as, Impera and Rigoli in [5].
Cite
@article{arxiv.2501.11614,
title = {Rigidity and nonexistence of complete spacelike hypersurfaces in the steady state space},
author = {Weiller F. C. Barboza and Henrique F. de Lima and Marco Antonio L. Velásquez},
journal= {arXiv preprint arXiv:2501.11614},
year = {2025}
}