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arXiv · 1003.0338

$r$-Stable Hypersurfaces in Conformally Stationary Spacetimes

F. Camargo·A. Caminha·H. de Lima·M. Velásquez
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Abstract

In this paper we study the r-stability of closed spacelike hypersurfaces with constant $r$-th mean curvature in conformally stationary spacetimes of constant sectional curvature. In this setting, we obtain a characterization of $r-$stability through the analysis of the first eigenvalue of an operator naturally attached to the $r$-th mean curvature. As an application, we treat the case in which the spacetime is the de Sitter space.

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F. Camargo, A. Caminha, H. de Lima, M. Velásquez. 2010-03-01. $r$-Stable Hypersurfaces in Conformally Stationary Spacetimes. https://arxiv.org/abs/1003.0338

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