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AQUINO, C. P.; LIMA, H. F. DE. UNIQUENESS OF COMPLETE HYPERSURFACES WITH BOUNDED HIGHER ORDER MEAN CURVATURES IN SEMI-RIEMANNIAN WARPED PRODUCTS. Glasgow mathematical journal, Tome 54 (2012) no. 1, pp. 201-212. doi: 10.1017/S0017089511000541
@article{10_1017_S0017089511000541,
author = {AQUINO, C. P. and LIMA, H. F. DE},
title = {UNIQUENESS {OF} {COMPLETE} {HYPERSURFACES} {WITH} {BOUNDED} {HIGHER} {ORDER} {MEAN} {CURVATURES} {IN} {SEMI-RIEMANNIAN} {WARPED} {PRODUCTS}},
journal = {Glasgow mathematical journal},
pages = {201--212},
year = {2012},
volume = {54},
number = {1},
doi = {10.1017/S0017089511000541},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089511000541/}
}
TY - JOUR AU - AQUINO, C. P. AU - LIMA, H. F. DE TI - UNIQUENESS OF COMPLETE HYPERSURFACES WITH BOUNDED HIGHER ORDER MEAN CURVATURES IN SEMI-RIEMANNIAN WARPED PRODUCTS JO - Glasgow mathematical journal PY - 2012 SP - 201 EP - 212 VL - 54 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089511000541/ DO - 10.1017/S0017089511000541 ID - 10_1017_S0017089511000541 ER -
%0 Journal Article %A AQUINO, C. P. %A LIMA, H. F. DE %T UNIQUENESS OF COMPLETE HYPERSURFACES WITH BOUNDED HIGHER ORDER MEAN CURVATURES IN SEMI-RIEMANNIAN WARPED PRODUCTS %J Glasgow mathematical journal %D 2012 %P 201-212 %V 54 %N 1 %U http://geodesic.mathdoc.fr/articles/10.1017/S0017089511000541/ %R 10.1017/S0017089511000541 %F 10_1017_S0017089511000541
[1] 1.Albujer, A. L. and Alías, L. J., Spacelike hypersurfaces with constant mean curvature in the steady state space, Proc. Amer. Math. Soc. 137 (2009), 711–721. Google Scholar | DOI
[2] 2.Alías, L. J. and Colares, A. G., Uniqueness of space-like hypersurfaces with constant higher order mean curvature in generalized Robertson–Walker spacetimes, Math. Proc. Camb. Philos. Soc. 143 (2007), 703–729. Google Scholar
[3] 3.Alías, L. J. and Dajczer, M., Uniqueness of constant mean curvature surfaces properly immersed in a slab, Comment. Math. Helv. 81 (2006), 653–663. Google Scholar | DOI
[4] 4.Alías, L. J., Dajczer, M. and Ripoll, J., A Bernstein-type theorem for Riemannian manifolds with a Killing field, Ann. Global Anal. Geom. 31 (2007), 363–373. Google Scholar | DOI
[5] 5.Alías, L. J., Romero, A. and Sánchez, M., Uniqueness of complete space-like hypersurfaces with constant mean curvature in Generalized Robertson–Walker spacetimes, Gen. Relat. Grav. 27 (1995), 71–84. Google Scholar
[6] 6.Barbosa, J. L. M. and Colares, A. G., Stability of hypersurfaces with constant r-mean curvature, Ann. Global Anal. Geom. 15 (1997), 277–297. Google Scholar
[7] 7.Bondi, H. and Gold, T., On the generation of magnetism by fluid motion, Month. Not. Roy. Astr. Soc. 108 (1948), 252–270. Google Scholar
[8] 8.Camargo, F. E. C., Caminha, A. and de Lima, H. F., Bernstein-type theorems in semi-Riemannian warped products, Proc. Amer. Math. Soc. 139 (2011), 1841–1850. Google Scholar
[9] 9.Caminha, A. and de Lima, H. F., Complete vertical graphs with constant mean curvature in semi-Riemannian warped products, Bull. Belgian Math. Soc. 16 (2009), 91–105. Google Scholar
[10] 10.Caminha, A. and de Lima, H. F., Complete space-like hypersurfaces in conformally stationary Lorentz manifolds, Gen. Relativ. Gravit. 41 (2009), 173–189. Google Scholar | DOI
[11] 11.Cheng, S. Y. and Yau, S. T., Hypersurfaces with constant scalar curvature, Math. Ann. 225 (1977), 195–204. Google Scholar | DOI
[12] 12.Colares, A. G. and de Lima, H. F., On the rigidity of spacelike hypersurfaces immersed in the steady state space , to appear in Publ. Math. Debrecen (2011). Google Scholar
[13] 13.de Lima, H. F., Rigidity theorems in the hyperbolic space, preprint (2010). Google Scholar
[14] 14.Hawking, S. W. and Ellis, G. F. R., The large scale structure of spacetime (Cambridge University Press, Cambridge, UK, 1973). Google Scholar
[15] 15.Hoyle, F., A new model for the expanding universe, Month. Not. Roy. Astr. Soc. 108 (1948), 372–382. Google Scholar
[16] 16.López, R. and Montiel, S., Existence of constant mean curvature graphs in hyperbolic space, Calc. Var. 8 (1999), 177–190. Google Scholar
[17] 17.Montiel, S., An integral inequality for compact space-like hypersurfaces in de Sitter space and applications to the case of constant mean curvature, Indiana Univ. Math. J. 37 (1988), 909–917. Google Scholar
[18] 18.Montiel, S., Unicity of constant mean curvature hypersurfaces in some Riemannian manifolds, Indiana Univ. Math. J. 48 (1999), 711–748. Google Scholar | DOI
[19] 19.Montiel, S., Uniqueness of space-like hypersurfaces of constant mean curvature in foliated spacetimes, Math. Ann. 314 (1999), 529–553. Google Scholar
[20] 20.Montiel, S., Complete non-compact space-like hypersurfaces of constant mean curvature in de Sitter Space, J. Math. Soc. Japan. 55 (2003), 915–938. Google Scholar
[21] 21.Omori, H., Isometric immersions of Riemannian manifolds, J. Math. Soc. Japan 19 (1967), 205–214. Google Scholar
[22] 22.O'Neill, B., Semi-Riemannian geometry, with applications to relativity (Academic Press, New York 1983). Google Scholar
[23] 23.Rosenberg, H., Hypersurfaces of constant curvature in space forms, Bull. Sc. Math. 117 (1993), 217–239. Google Scholar
[24] 24.Weinberg, S., Gravitation and cosmology: Principles and applications of the general theory of relativity (John Wiley, New York, 1972). Google Scholar
[25] 25.Yau, S. T., Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201–228. Google Scholar | DOI
[26] 26.Yau, S. T., Some function-theoretic properties of complete Riemannian manifolds and their applications to geometry, Indiana Univ. Math. J. 25 (1976), 659–670. Google Scholar | DOI
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