Local foliations and optimal regularity of Einstein spacetimes

Journal of Geometry and Physics - Tập 59 - Trang 913-941 - 2009
Bing-Long Chen1, Philippe G. LeFloch2
1Department of Mathematics, Sun Yat-sen University, Guangzhou, People’s Republic of China
2Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientifique, Université Pierre et Marie Curie (Paris 6), 4 Place Jussieu, 75252 Paris, France

Tài liệu tham khảo

Chen, 2008, Injectivity radius estimates for Lorentzian manifolds, Comm. Math. Phys., 278, 679, 10.1007/s00220-008-0412-x Bartnik, 1982, Spacelike hypersurfaces with prescribed boundary values and mean curvature, Comm. Math. Phys., 87, 131, 10.1007/BF01211061 Gerhardt, 1983, H-surfaces in Lorentzian manifolds, Comm. Math. Phys., 89, 523, 10.1007/BF01214742 Andersson, 2003, Elliptic-hyperbolic systems and the Einstein equations, Ann. Inst. Henri Poincaré, 4, 1, 10.1007/s00023-003-0120-1 Andersson, 2004, Future complete vacuum spacetimes, 299 Andersson, 2004, Bel-Robinson energy and constant mean-curvature foliations, Ann. Henri Poincaré, 5, 235, 10.1007/s00023-004-0167-7 M. Reiris, The constant mean curvature Einstein flow and the Bel-Robinson energy, Preprint, ArXiv:0705.3070 Klainerman, 2008, On the radius of injectivity of null hypersurfaces, J. Amer. Math. Soc., 21, 775, 10.1090/S0894-0347-08-00592-4 S. Klainerman, I. Rodnianski, On the breakdown criterion in general relativity, Preprint, 2008 DeTurck, 1981, Some regularity theorems in Riemannian geometry, Ann. Sci. École Norm. Sup., 14, 249, 10.24033/asens.1405 Jost, 1982, Geometrische Methoden zur Gewinnung von a-priori-Schranken für harmonische Abbildungen, Manuscripta Math., 40, 27, 10.1007/BF01168235 Anderson, 2003, Regularity for Lorentz metrics under curvature bounds, J. Math. Phys., 44, 2994, 10.1063/1.1580199 Besse, 1987, vol. 3 Hawking, 1973 O’Neill, 1983 Simons, 1968, Minimal varieties in Riemannian manifolds, Ann. Math., 88, 62, 10.2307/1970556 Cheeger, 1982, Finite propagation speed kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Differential Geom., 17, 15, 10.4310/jdg/1214436699 Gilbarg, 1983