About the parabolicity of trapped submanifolds in standard static spacetimes. (October 2020)

• Record Type: Journal Article
• Authors: Andrade, Maria; Lima, Eraldo Almeida; Roing, Fernanda
• Is Part Of: Nonlinear analysis. Volume 199(2020)
• Publication Date: 2020-10
• Subjects: primary 53C42 -- secondary 53B30 and 53C50; Standard static spacetimes -- Weakly trapped submanifolds -- Parabolic spacelike submanifolds -- Mean curvature vector field; 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.2020.112037
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this work, we introduce the concept of totally trapped submanifolds immersed in a Lorentzian manifold. Moreover, we obtain some uniqueness or non-existence results for ( p, ψ ) -parabolic submanifolds immersed in standard static spacetimes (SSST). In particular, we derive some rigidity results for this type of submanifolds which guarantee that, under appropriate hypothesis, the only ones are those contained in slices. In order to obtain these results we study the height function associated to the submanifold using the ( p, ψ ) -Laplacian for ψ a function associated to the warping function of the SSST.