Tohoku Mathematical Journal

Compact spacelike surfaces with constant mean curvature in the Lorentz-Minkowski $3$-space

Luis J. Alías, Rafael López, and José A. Pastor

Full-text: Open access

Article information

Tohoku Math. J. (2), Volume 50, Number 4 (1998), 491-501.

First available in Project Euclid: 3 May 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


Alías, Luis J.; López, Rafael; Pastor, José A. Compact spacelike surfaces with constant mean curvature in the Lorentz-Minkowski $3$-space. Tohoku Math. J. (2) 50 (1998), no. 4, 491--501. doi:10.2748/tmj/1178224893.

Export citation


  • [1] K AKUTAGAWA AND S. NISHIKAWA, The Gauss map and spacelike surfaces with prescribed mean curvature in Minkowski 3-space, Thoku Math J 42 (1990), 67-82
  • [2] A D ALEXANDROV, A characteristic property of spheres, Ann Mat Pura Appl 58 (1962), 303-31
  • [3] R BARTNIK AND L. SIMON, Spacelike hypersurfaces with prescribed boundary values and mea curvature, Comm Math Phys 87 (1982), 131-152
  • [4] F BRITO, R SAEARP, W H MEEKS III AND H. ROSENBERG, Structure theorems for constant mea curvature surfaces bounded by a planar curve, Indiana Univ Math J 40 (1991), 333-343
  • [5] Y CHOQUET-BRUHAT AND J. YORK, The Cauchy Problem, in: General Relativity and Gravitation Held (ed), Plenum Press, New York, 1980
  • [6] D GILBARG AND N. S TRUDINGER, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1983
  • [7] H HEINZ, On the nonexistence of a surface of constant mean curvature with finite area and prescribe rectificable boundary, Arch Rational Mech Anal 35 (1969), 249-252
  • [8] N KAPOULEAS, Compact constant mean curvature surfaces in Euclidean three-space, J Differentia Geom 33 (1991), 683-715
  • [9] M Koiso, Symmetry of hypersurfaces of constant mean curvature with symmetric boundary, Mat Z 191 (1986), 567-574
  • [10] N KOREVAAR, R KUSNER AND B. SoLOMOM, The structure of complete embedded surfaces with constan mean curvature, J Differential Geom 30 (1989), 465-503
  • [11] R LOPEZ AND S. MONTIEL, Constant mean curvature discs with bounded area, Proc Amer Mat Soc 123 (1995), 1555-1558
  • [12] R LOPEZ AND S. MONTIEL, Constant mean curvature surfaces with planar boundary, Duke Math 85 (1996), 583-604
  • [13] J E MARSDEN AND F. J TIPLER, Maximal hypersurfaces and foliations of constant mean curvatur in general relativity, Phys Rep 66 (1980), 109-139
  • [14] A Ros AND H. ROSENBERG, Constant mean curvature surfaces in a half-space of R3 with boundar in the boundary of the half-space, J Differential Geom 44 (1996), 807-817
  • [15] A TREIBERGS, Entire spacelike hypersurfaces of constant mean curvature in Minkowski space, Inven Math 66 (1982), 39-56
  • [16] T Y WAN, Constant mean curvature surfaces, harmonic maps, and universal Teichmuller space, Differential Geom 35 (1992), 643-657