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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ジャーナルフリー

1989 年 41 巻 1 号 p. 161-172

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

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Published: 1989 Received: 1987/09/21 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: 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.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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