Tohoku Mathematical Journal

Spacelike hypersurfaces of constant mean curvature and Calabi-Bernstein type problems

Luis J. Alías, Alfonso Romero, and Miguel Sánchez

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Tohoku Math. J. (2), Volume 49, Number 3 (1997), 337-345.

First available in Project Euclid: 3 May 2007

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Zentralblatt MATH identifier

Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
Secondary: 35J60: Nonlinear elliptic equations 53C50: Lorentz manifolds, manifolds with indefinite metrics


Alías, Luis J.; Romero, Alfonso; Sánchez, Miguel. Spacelike hypersurfaces of constant mean curvature and Calabi-Bernstein type problems. Tohoku Math. J. (2) 49 (1997), no. 3, 337--345. doi:10.2748/tmj/1178225107.

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  • [1] K. AKUTAGAWA, On spacelike hypersurfaces with constant mean curvature in the de Sitter space, Math. Z. 196 (1987), 13-19.
  • [2] L. J. ALIAS, A. ROMERO AND M. SANCHEZ, Uniqueness of complete spacelike hypersurfaces of constan mean curvature in Generalized Robertson-Walker spacetimes, Gen. Relativity Gravitation 27 (1995), 71-84.
  • [3] L. J. ALIAS, A. ROMERO AND M. SANCHEZ, Spacelike hypersurfaces of constant mean curvature i spatially closed Lorentzian manifolds, Anales de Fisica, WOGDA'94, Proceedings of the Third Fall Workshop: Differential Geometry and its Applications (1995), 177-187.
  • [4] A. L. BESSE, Einstein Manifolds, Springer-Verlag, Berlin 1987
  • [5] E. CALABI, Examples of Bernstein problems for some nonlinear equations, Proc. Sympos. Pure Math 15 (1968), 223-230.
  • [6] S. -Y. CHENG AND S. -T. YAU, Maximal spacelike hypersurfaces in the Lorentz-Minkowski spaces, Ann of Math. 104 (1976), 407-419.
  • [7] Y. CHOQUET-BRUHAT, Quelques proprietes des sous-varietes maximales d'une variete lorentzienne, C. R. Acad. Sci. Paris, Ser. A, 281 (1975), 577-580.
  • [8] A. J. GODDARD, Some remarks on the existence of spacelike hypersurfaces of constant mean curvature, Math. Proc. Cambridge Philos. Soc. 82 (1977), 489-495.
  • [9] S. MONTIEL, An integral inequality for compact spacelike hypersurfaces in de Sitter space an applications to the case of constant mean curvature, Indiana Univ. Math. J. 37 (1988), 909-917.
  • [10] B. O'NEILL, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983.
  • [11] S. STUMBLES, Hypersurfaces of constant mean extrinsic curvature, Ann. Physics 133 (1981), 28-56
  • [12] A. TREIBERGS, Entire spacelike hypersurfaces of constant mean curvature in Minkowski space, Invent Math. 66 (1982), 39-52.
  • [13] K. YANO, On harmonic and Killing vector fields, Ann. of Math. 55 (1952), 38^5
  • [14] S. -T. YAU, Calabi's conjecture and some new results in algebraic geometry, Proc. Nat. Acad. Sci U. S. A. 74 (1977), 1798-1799.