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arXiv · 2501.11614

Rigidity and nonexistence of complete spacelike hypersurfaces in the steady state space

Weiller F. C. Barboza·Henrique F. de Lima·Marco Antonio L. Velásquez
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Abstract

We study complete spacelike hypersurfaces immersed in an open region of the de Sitter space $\mathbb{S}^{n+1}_{1}$ which is known as the steady state space $\mathcal{H}^{n+1}$. 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 $\mathcal{H}^{n+1}$. 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].

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Weiller F. C. Barboza, Henrique F. de Lima, Marco Antonio L. Velásquez. 2025-01-20. Rigidity and nonexistence of complete spacelike hypersurfaces in the steady state space. https://arxiv.org/abs/2501.11614

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