Letters in Mathematical Physics

, Volume 93, Issue 1, pp 85–105 | Cite as

Constant Mean Curvature Spacelike Surfaces in Three-Dimensional Generalized Robertson–Walker Spacetimes

  • Magdalena Caballero
  • Alfonso Romero
  • Rafael M. Rubio


Several uniqueness and non-existence results on complete constant mean curvature spacelike surfaces lying between two slices in certain three-dimensional generalized Robertson–Walker spacetimes are given. They are obtained from a local integral estimation of the squared length of the gradient of a distinguished smooth function on a constant mean curvature spacelike surface, under a suitable curvature condition on the ambient spacetime. As a consequence, all the entire bounded solutions to certain family of constant mean curvature spacelike surface differential equations are found.

Mathematics Subject Classification (2000)

53C42 53C50 35J60 


spacelike surfaces constant mean curvature Calabi–Bernstein problem generalized Robertson–Walker spacetimes 


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Copyright information

© Springer 2010

Authors and Affiliations

  • Magdalena Caballero
    • 1
  • Alfonso Romero
    • 2
  • Rafael M. Rubio
    • 1
  1. 1.Departamento de Matemáticas, Campus de RabanalesUniversidad de CórdobaCórdobaSpain
  2. 2.Departamento de Geometría y TopologíaUniversidad de GranadaGranadaSpain

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