Weak maximum principles and geometric estimates for spacelike hypersurfaces in generalized Robertson–Walker spacetimes. (December 2015)

• Record Type: Journal Article
• Authors: Alías, Luis J.; Rigoli, Marco; Scoleri, Simona
• Is Part Of: Nonlinear analysis. Volume 129(2015)
• Page Start: 119
• Page End: 142
• Publication Date: 2015-12
• Subjects: 53C40 -- 53C42; Generalized Robertson–Walker spacetimes -- Weak maximum principle -- Spacelike graphs -- Lorentzian mean curvature operator; 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.2015.08.018
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we deal with complete spacelike hypersurfaces in a generalized Robertson–Walker spacetime. Using as main analytical tool a new local form of the weak maximum principle for a class of operators including the Lorentzian mean curvature operator, we obtain some mean curvature estimates and height estimates for spacelike graphs with nice Bernstein type consequences. We also give height estimates for spacelike hypersurfaces with constant higher order mean curvature, which are obtained via the local form of the weak maximum principle recently given in Alías et al. (in press) for a class of operators including those constructed from the Newton tensors of a hypersurface.