Abstract
In this paper, we establish the notion of strong (r, s)-stability concerning closed space-like hypersurfaces immersed with higher-order mean curvatures linearly related in the de Sitter space . In this setting, we prove that totally umbilical round spheres of are strongly (r, s)-stable. Afterwards, we obtain sufficient geometric conditions that guarantee that a closed strongly (r, s)-stable space-like hypersurface in must be a totally umbilical round sphere.
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