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Spacelike hypersurfaces of constant mean curvature and Calabi-Bernstein type problems. (English) Zbl 0912.53046
Authors’ abstract: “Spacelike graphs of constant mean curvature over compact Riemannian manifolds in Lorentzian manifolds with constant sectional curvature are studied. The corresponding Calabi-Bernstein type problems are stated. In the case of nonpositive sectional curvature, all their solutions are obtained, and for positive sectional curvature well-known results are extended”.

53C42Immersions (differential geometry)
53C50Lorentz manifolds, manifolds with indefinite metrics
Full Text: DOI
[1] K. AKUTAGAWA, On spacelike hypersurfaces with constant mean curvature in the de Sitter space, Math. Z. 196 (1987), 13-19. · Zbl 0611.53047 · doi:10.1007/BF01179263 · eudml:173859
[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. · Zbl 0908.53034 · doi:10.1007/BF02105675
[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. · Zbl 0838.53048
[4] A. L. BESSE, Einstein Manifolds, Springer-Verlag, Berlin 1987 · Zbl 0613.53001
[5] E. CALABI, Examples of Bernstein problems for some nonlinear equations, Proc. Sympos. Pure Math 15 (1968), 223-230. · Zbl 0211.12801
[6] S. -Y. CHENG AND S. -T. YAU, Maximal spacelike hypersurfaces in the Lorentz-Minkowski spaces, Ann of Math. 104 (1976), 407-419. JSTOR: · Zbl 0352.53021 · doi:10.2307/1970963 · http://links.jstor.org/sici?sici=0003-486X%28197611%292%3A104%3A3%3C407%3AMSHITL%3E2.0.CO%3B2-9&origin=euclid
[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. · Zbl 0324.53046
[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. · Zbl 0386.53042 · doi:10.1017/S0305004100054153
[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. · Zbl 0677.53067 · doi:10.1512/iumj.1988.37.37045
[10] B. O’NEILL, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983. · Zbl 0531.53051
[11] S. STUMBLES, Hypersurfaces of constant mean extrinsic curvature, Ann. Physics 133 (1981), 28-56 · Zbl 0472.53063 · doi:10.1016/0003-4916(81)90240-2
[12] A. TREIBERGS, Entire spacelike hypersurfaces of constant mean curvature in Minkowski space, Invent Math. 66 (1982), 39-52. · Zbl 0483.53055 · doi:10.1007/BF01404755 · eudml:142868
[13] K. YANO, On harmonic and Killing vector fields, Ann. of Math. 55 (1952), 38^5 JSTOR: · Zbl 0046.15603 · doi:10.2307/1969418 · http://links.jstor.org/sici?sici=0003-486X%28195201%292%3A55%3A1%3C38%3AOHAKVF%3E2.0.CO%3B2-8&origin=euclid
[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. JSTOR: · Zbl 0355.32028 · doi:10.1073/pnas.74.5.1798 · http://links.jstor.org/sici?sici=0027-8424%28197705%2974%3A5%3C1798%3ACCASNR%3E2.0.CO%3B2-H&origin=euclid