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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Aledo, Juan A. Rubio, Rafael M. and Salamanca, Juan J. 2016. Complete spacelike hypersurfaces in generalized Robertson–Walker and the null convergence condition: Calabi–Bernstein problems. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas,


    Cavalcante, M. P. de Lima, H. F. and Santos, M. S. 2015. New Calabi–Bernstein type results in weighted generalized Robertson–Walker spacetimes. Acta Mathematica Hungarica, Vol. 145, Issue. 2, p. 440.


    Aquino, C. P. and de Lima, H. F. 2014. On the Unicity of Complete Hypersurfaces Immersed in a Semi-Riemannian Warped Product. The Journal of Geometric Analysis, Vol. 24, Issue. 2, p. 1126.


    de Lima, Henrique Fernandes and Velásquez, Marco Antonio Lázaro 2014. Uniqueness of complete spacelike hypersurfaces via their higher order mean curvatures in a conformally stationary spacetime. Mathematische Nachrichten, Vol. 287, Issue. 11-12, p. 1223.


    Alías, Luis J. Colares, Antonio Gervásio and de Lima, Henrique F. 2013. On the rigidity of complete spacelike hypersurfaces immersed in a generalized Robertson-Walker spacetime. Bulletin of the Brazilian Mathematical Society, New Series, Vol. 44, Issue. 2, p. 195.


    de Lima, Henrique F. and Parente, Ulisses L. 2013. On the geometry of maximal spacelike hypersurfaces immersed in a generalized Robertson–Walker spacetime. Annali di Matematica Pura ed Applicata, Vol. 192, Issue. 4, p. 649.


    Wang, Wenjie and Liu, Ximin 2013. On Bernstein-Type Theorems in Semi-Riemannian Warped Products. Advances in Mathematical Physics, Vol. 2013, p. 1.


    Wang, Yaning and Liu, Ximin 2013. On Complete Spacelike Hypersurfaces in a Semi-Riemannian Warped Product. Journal of Applied Mathematics, Vol. 2013, p. 1.


    CAMARGO, FERNANDA CAMINHA, ANTONIO DE LIMA, HENRIQUE and PARENTE, ULISSES 2012. Generalized maximum principles and the rigidity of complete spacelike hypersurfaces. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 153, Issue. 03, p. 541.


    de Lima, Henrique F. and de Lima, Joseílson R. 2012. Complete hypersurfaces immersed in a semi-Riemannian warped product. Differential Geometry and its Applications, Vol. 30, Issue. 1, p. 136.


    de Lima, Henrique Fernandes 2012. On Bernstein-type properties of complete spacelike hypersurfaces immersed in a generalized Robertson–Walker spacetime. Journal of Geometry, Vol. 103, Issue. 2, p. 219.


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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 151, Issue 2
  • September 2011, pp. 271-282

Complete spacelike hypersurfaces in a Robertson–Walker spacetime

  • ALMA L. ALBUJER (a1), FERNANDA E. C. CAMARGO (a2) and HENRIQUE F. DE LIMA (a3)
  • DOI: http://dx.doi.org/10.1017/S0305004111000351
  • Published online: 13 July 2011
Abstract
Abstract

In this paper, as a suitable application of the well-known generalized maximum principle of Omori–Yau, we obtain uniqueness results concerning to complete spacelike hypersurfaces with constant mean curvature immersed in a Robertson–Walker (RW) spacetime. As an application of such uniqueness results for the case of vertical graphs in a RW spacetime, we also get non-parametric rigidity results.

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[12]M. Caballero , A. Romero and R. M. Rubio Constant mean curvature spacelike surfaces in three-dimensional generalized Robertson–Walker spacetimes. Lett. Math. Phys. 93 (2010), 85105.

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[20]M. Rainer and H-J. Schmidt Inhomogeneous cosmological models with homogeneous inner hypersurface geometry. Gen. Relativity Gravitation 27 (1995), 12651293.

[21]A. Romero and R. M. Rubio On the mean curvature of spaclike surfaces in certain three-dimensional Robertson–Walker spacetimes and Calabi–Bernstein's type problems. Ann. Glob. Anal. Geom. 37 (2010), 2131.

[22]Y. L. Xin On the Gauss image of a spacelike hypersurface with constant mean curvature in Minkowski space. Comment. Math. Helv. 66 (1991), 590598.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
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