Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 3
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Aquino, Cícero P. Araújo, Jogli G. and de Lima, Henrique F. 2016. Rigidity of complete hypersurfaces in warped product spaces via higher order mean curvatures. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 57, Issue. 2, p. 391.

    Aquino, Cícero P. de Lima, Henrique F. dos Santos, Fábio R. and Velásquez, Marco Antonio L. 2015. Spacelike hypersurfaces with constant rth mean curvature in steady state type spacetimes. Journal of Geometry, Vol. 106, Issue. 1, p. 85.

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



  • C. P. AQUINO (a1) (a2) and H. F. DE LIMA (a3)
  • DOI:
  • Published online: 09 December 2011

In this paper, we deal with complete hypersurfaces immersed with bounded higher order mean curvatures in steady state-type spacetimes and in hyperbolic-type spaces. By applying a generalised maximum principle for the Yau's square operator [11], we obtain uniqueness results in each of these ambient spaces.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

1.A. L. Albujer and L. J. Alías , Spacelike hypersurfaces with constant mean curvature in the steady state space, Proc. Amer. Math. Soc. 137 (2009), 711721.

4.L. J. Alías , M. Dajczer and J. Ripoll , A Bernstein-type theorem for Riemannian manifolds with a Killing field, Ann. Global Anal. Geom. 31 (2007), 363373.

5.L. J. Alías , A. Romero and M. Sánchez , Uniqueness of complete space-like hypersurfaces with constant mean curvature in Generalized Robertson–Walker spacetimes, Gen. Relat. Grav. 27 (1995), 7184.

6.J. L. M. Barbosa and A. G. Colares , Stability of hypersurfaces with constant r-mean curvature, Ann. Global Anal. Geom. 15 (1997), 277297.

7.H. Bondi and T. Gold , On the generation of magnetism by fluid motion, Month. Not. Roy. Astr. Soc. 108 (1948), 252270.

8.F. E. C. Camargo , A. Caminha and H. F. de Lima , Bernstein-type theorems in semi-Riemannian warped products, Proc. Amer. Math. Soc. 139 (2011), 18411850.

10.A. Caminha and H. F. de Lima , Complete space-like hypersurfaces in conformally stationary Lorentz manifolds, Gen. Relativ. Gravit. 41 (2009), 173189.

11.S. Y. Cheng and S. T. Yau , Hypersurfaces with constant scalar curvature, Math. Ann. 225 (1977), 195204.

15.F. Hoyle , A new model for the expanding universe, Month. Not. Roy. Astr. Soc. 108 (1948), 372382.

17.S. Montiel , An integral inequality for compact space-like hypersurfaces in de Sitter space and applications to the case of constant mean curvature, Indiana Univ. Math. J. 37 (1988), 909917.

18.S. Montiel , Unicity of constant mean curvature hypersurfaces in some Riemannian manifolds, Indiana Univ. Math. J. 48 (1999), 711748.

19.S. Montiel , Uniqueness of space-like hypersurfaces of constant mean curvature in foliated spacetimes, Math. Ann. 314 (1999), 529553.

20.S. Montiel , Complete non-compact space-like hypersurfaces of constant mean curvature in de Sitter Space, J. Math. Soc. Japan. 55 (2003), 915938.

21.H. Omori , Isometric immersions of Riemannian manifolds, J. Math. Soc. Japan 19 (1967), 205214.

25.S. T. Yau , Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201228.

26.S. T. Yau , Some function-theoretic properties of complete Riemannian manifolds and their applications to geometry, Indiana Univ. Math. J. 25 (1976), 659670.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
Please enter your name
Please enter a valid email address
Who would you like to send this to? *