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Spacelike Hypersurfaces in Spatially Parabolic Standard Static Spacetimes and Calabi–Bernstein-Type Problems

  • José A. S. PelegrínEmail author
  • Alfonso Romero
  • Rafael M. Rubio
Article

Abstract

Complete spacelike hypersurfaces in spatially parabolic standard static spacetimes are studied. Under natural boundedness assumptions, we show how the parabolicity of the base is inherited by any spacelike hypersurface and vice versa. Moreover, we give new uniqueness and non-existence results for complete spacelike hypersurfaces in these ambient spacetimes as well as solve new Calabi–Bernstein-type problems.

Keywords

Spacelike hypersurface parabolicity standard static spacetime Calabi–Bernstein problem 

Mathematics Subject Classification

53C42 53C80 53C50 58J05 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Departamento de Geometría y TopologíaUniversidad de GranadaGranadaSpain
  2. 2.Departamento de Matemáticas, Campus de RabanalesUniversidad de CórdobaCórdobaSpain
  3. 3.Departamento de Matemática Aplicada y EstadísticaUniversidad CEU San PabloMadridSpain

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