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

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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.

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Authors and Affiliations

  1. Departamento de Matemáticas, Campus Universitario de Rabanales, Universidad de Córdoba, 14071, Córdoba, Spain

    Alma L. Albujer

  2. Departamento de Matemática, Universidade Federal de Campina Grande, Campina Grande, Paraíba , 58429-970, Brazil

    Henrique F. de Lima, Arlandson M. Oliveira & Marco Antonio L. Velásquez

Authors
  1. Alma L. Albujer
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  2. Henrique F. de Lima
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  3. Arlandson M. Oliveira
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  4. Marco Antonio L. Velásquez
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Correspondence to Henrique F. de Lima.

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Albujer, A.L., de Lima, H.F., Oliveira, A.M. et al. \(\phi \)-Parabolicity and the Uniqueness of Spacelike Hypersurfaces Immersed in a Spatially Weighted GRW Spacetime. Mediterr. J. Math. 15, 84 (2018). https://doi.org/10.1007/s00009-018-1134-8

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  • DOI: https://doi.org/10.1007/s00009-018-1134-8

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