Stable maximal hypersurfaces in Lorentzian spacetimes. (February 2019)

• Record Type: Journal Article
• Authors: Colombo, Giulio; Pelegrín, José A.S.; Rigoli, Marco
• Is Part Of: Nonlinear analysis. Volume 179(2019)
• Page Start: 354
• Page End: 382
• Publication Date: 2019-02
• Subjects: 53C42 -- 53C50 -- 83C99 -- 53C80; Stable maximal hypersurface -- k-stability -- Spacetime of constant sectional curvature -- Generalized Robertson–Walker spacetime; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.09.009
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the geometry of stable maximal hypersurfaces in a variety of spacetimes satisfying various physically relevant curvature assumptions, for instance the Timelike Convergence Condition (TCC). We characterize stability when the target space has constant sectional curvature as well as give sufficient conditions on the geometry of the ambient spacetime (e.g., the validity of TCC) to ensure stability. Some rigidity results and height estimates are also proven in GRW spacetimes. In the last part of the paper we consider k -stability of spacelike hypersurfaces, a concept related to mean curvatures of higher orders.