\(\phi \)-Parabolicity and the Uniqueness of Spacelike Hypersurfaces Immersed in a Spatially Weighted GRW Spacetime

  • Alma L. Albujer
  • Henrique F. de Lima
  • Arlandson M. Oliveira
  • Marco Antonio L. Velásquez
Article
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Abstract

In this paper, we extend a technique due to Romero et al. (Class Quantum Gravity 30:1–13, 2013; Int J Geom Methods Mod Phys 10:1360014, 2013; J Math Anal Appl 419:355–372, 2014) establishing sufficient conditions to guarantee the parabolicity of complete spacelike hypersurfaces immersed in a weighted generalized Robertson–Walker spacetime whose fiber has \(\phi \)-parabolic universal Riemannian covering. As some applications of this criteria, we obtain uniqueness results concerning spacelike hypersurfaces immersed in spatially weighted generalized Robertson–Walker spacetimes. Furthermore, Calabi–Bernstein type results are also given.

Keywords

Spatially weighted generalized Robertson–Walker spacetimes Bakry–Émery–Ricci tensor Drifted Laplacian \(\phi \)-Parabolicity Weighted mean curvature Complete spacelike hypersurfaces Entire vertical graphs 

Mathematics Subject Classification

Primary 53C42 53A07 Secondary 35P15 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Alma L. Albujer
    • 1
  • Henrique F. de Lima
    • 2
  • Arlandson M. Oliveira
    • 2
  • Marco Antonio L. Velásquez
    • 2
  1. 1.Departamento de Matemáticas, Campus Universitario de RabanalesUniversidad de CórdobaCórdobaSpain
  2. 2.Departamento de MatemáticaUniversidade Federal de Campina GrandeCampina GrandeBrazil

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