Kodai Mathematical Journal

r-stable spacelike hypersurfaces in conformally stationary spacetimes

Fernanda Camargo, Antonio Caminha, Henrique Fernandes de Lima, and Marco Antonio Velásquez

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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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Kodai Math. J., Volume 34, Number 3 (2011), 339-351.

First available in Project Euclid: 10 November 2011

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Camargo, Fernanda; Caminha, Antonio; de Lima, Henrique Fernandes; Velásquez, Marco Antonio. r -stable spacelike hypersurfaces in conformally stationary spacetimes. Kodai Math. J. 34 (2011), no. 3, 339--351. doi:10.2996/kmj/1320935545. https://projecteuclid.org/euclid.kmj/1320935545

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