New Calabi–Bernstein type results in Lorentzian product spaces with density. (August 2020)

• Record Type: Journal Article
• Authors: Aquino, Cícero P.; Baltazar, Halyson I.; de Lima, Henrique F.
• Is Part Of: Nonlinear analysis. Volume 197(2020)
• Publication Date: 2020-08
• Subjects: primary 53C42 53A07 -- secondary 35P15; Weighted Lorentzian product spaces -- Bakry–Émery–Ricci tensor -- Entire spacelike graphs; 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.2020.111855
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We investigate the rigidity of complete spacelike hypersurfaces immersed in a weighted Lorentzian product space of the type R 1 × P f n, endowed with a weight function f which does not depend on the parameter t ∈ R and whose Riemannian fiber P n has nonnegative Bakry–Émery–Ricci tensor. In this direction, supposing that the f -mean curvature is constant and assuming appropriate constraints on the norm of the gradient of f, we prove that such a spacelike hypersurface must be a slice of the ambient space. As application of our investigation, we obtain new Calabi–Bernstein type results concerning entire spacelike graphs constructed over P n . Our approach is based on an extension for the drift Laplacian of a generalized maximum principle of Akutagawa (1987) and a Liouville-type result due to Pigola et al. (2005).