Existence of maximal hypersurfaces in an asymptotically anti-de Sitter spacetime satisfying a global barrier condition

Kazuo AKUTAGAWA

doi:10.2969/jmsj/04110161

Kazuo AKUTAGAWA

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JOURNAL FREE ACCESS

1989 Volume 41 Issue 1 Pages 161-172

DOI https://doi.org/10.2969/jmsj/04110161

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Published: 1989 Received: September 21, 1987 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) R. Bartnik, Existence of maximal surfaces in asymptotically flat spacetimes, Comm. Math. Phys., 94 (1984), 155-175.
2) R. Bartnik and L. Simon, Spacelike hypersurfaces with prescribed boundary values and mean curvature, Comm. Math. Phys., 87 (1982), 131-152.
3) J. K. Beem and P. E. Ehrlich, Global Lorentzian geometry, Pure Appl. Math., 67, Dekker, New York, 1981.
4) J. K. Beem, P. E. Ehrlich, S. Markvosen and G. J. Galloway, Decomposition theorems for Lorentzian manifolds with nonpositive curvature, J. Differential Geom., 22 (1985), 29-42.
5) E. Calabi, Examples of Bernstein problems for some nonlinear equations, Proc. Sympos. Pure Appl. Math., 15 (1970), 223-230.
6) S.-Y. Cheng and S.-T. Yau, Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces, Ann. Math., 104 (1976), 407-419.
7) Y. Choquet-Bruhat, Maximal submanifolds with constant mean extrinsic curvature of a Lorentzian manifold, Ann. Scuola Norm. Sup. Pisa, 3(1976), 361-376.
8) D. Eardley and L. Smarr, Time functions in numerical relativity: Marginally bound dust collapse, Phys. Rev. D, 19 (1979), 2239-2259.
9) G. J. Galloway, Splitting theorems for spatially closed space-times, Comm. Math. Phys., 96 (1984), 423-429.
10) C. Gerhardt, H-surfaces in Lorentzian manifolds, Comm. Math. Phys., 89 (1983), 523-553.
11) D. Gilberg and N. Trudinger, Elliptic partial differential equations of second order, 2nd ed., Springer, 1983.
12) S. W. Hawking and G. F. Ellis, The large scale structure of space-time, Cambridge Univ. Press, 1973.
13) M. Henneaux and C. Teitelboim, Asymptotically anti-de Sitter spaces, Comm. Math. Phys., 98 (1985), 391-424.
14) R. Schoen and S.-T. Yau, Proof of the positive mass conjecture in general relativity, Comm. Math. Phys., 65 (1979), 45-76.
15) A. Treibergs, Entire spacelike hypersurfaces of constant mean curvature in Minkowski space, Invent. Math., 66 (1982), 39-56.

Right : [1] R. Bartnik, Existence of maximal surfaces in asymptotically flat spacetimes, Comm. Math. Phys., 94 (1984), 155-175.
[2] R. Bartnik and L. Simon, Spacelike hypersurfaces with prescribed boundary values and mean curvature, Comm. Math. Phys., 87 (1982), 131-152.
[3] J. K. Beem and P. E. Ehrlich, Global Lorentzian geometry, Pure Appl. Math., 67, Dekker, New York, 1981.
[4] J. K. Beem, P. E. Ehrlich, S. Markvosen and G. J. Galloway, Decomposition theorems for Lorentzian manifolds with nonpositive curvature, J. Differential Geom., 22 (1985), 29-42.
[5] E. Calabi, Examples of Bernstein problems for some nonlinear equations, Proc. Sympos. Pure Appl. Math., 15 (1970), 223-230.
[6] S. -Y. Cheng and S. -T. Yau, Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces, Ann. Math., 104 (1976), 407-419.
[7] Y. Choquet-Bruhat, Maximal submanifolds with constant mean extrinsic curvature of a Lorentzian manifold, Ann. Scuola Norm. Sup. Pisa, 3 (1976), 361-376.
[8] D. Eardley and L. Smarr, Time functions in numerical relativity: Marginally bound dust collapse, Phys. Rev. D, 19 (1979), 2239-2259.
[9] G. J. Galloway, Splitting theorems for spatially closed space-times, Comm. Math. Phys., 96 (1984), 423-429.
[10] C. Gerhardt, H-surfaces in Lorentzian manifolds, Comm. Math. Phys., 89 (1983), 523-553.
[11] D. Gilberg and N. Trudinger, Elliptic partial differential equations of second order, 2nd ed., Springer, 1983.
[12] S. W. Hawking and G. F. Ellis, The large scale structure of space-time, Cambridge Univ. Press, 1973.
[13] M. Henneaux and C. Teitelboim, Asymptotically anti-de Sitter spaces, Comm. Math. Phys., 98 (1985), 391-424.
[14] R. Schoen and S. -T. Yau, Proof of the positive mass conjecture in general relativity, Comm. Math. Phys., 65 (1979), 45-76.
[15] A. Treibergs, Entire spacelike hypersurfaces of constant mean curvature in Minkowski space, Invent. Math., 66 (1982), 39-56.

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