Strong (r, s)-stability in the de Sitter space. Issue 1 (30th January 2015) - de Lima, Henrique F.; de Sousa, Antonio F.; Velásquez, Marco Antonio L.
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.