Stabilité par déformation non-linéaire de la métrique de Minkowski [d'après D. Christodoulou et S. Klainerman]
Séminaire Bourbaki : volume 1990/91, exposés 730-744, Astérisque no. 201-202-203  (1991), Talk no. 740, p. 321-358
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     author = {Bourguignon, Jean-Pierre},
     title = {Stabilit\'e par d\'eformation non-lin\'eaire de la m\'etrique de Minkowski [d'apr\`es D. Christodoulou et S. Klainerman]},
     booktitle = {S\'eminaire Bourbaki : volume 1990/91, expos\'es 730-744},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {201-202-203},
     year = {1991},
     note = {talk:740},
     pages = {321-358},
     zbl = {0754.53060},
     mrnumber = {1157847},
     language = {fr},
     url = {http://www.numdam.org/item/SB_1990-1991__33__321_0}
}
Bourguignon, Jean-Pierre. Stabilité par déformation non-linéaire de la métrique de Minkowski [d'après D. Christodoulou et S. Klainerman], in Séminaire Bourbaki : volume 1990/91, exposés 730-744, Astérisque, no. 201-202-203 (1991), Talk no. 740, pp. 321-358. http://www.numdam.org/item/SB_1990-1991__33__321_0/

[1] R. Arnowitt, S. Deser, C. Misner, Coordinate invariance and energy expressions in General Relativity, Phys. Rev. 122 (1961), 997-1006. | MR 127946 | Zbl 0094.23003

[2] R. Bartnik, Existence of maximal surfaces in asymptotically flat space-times, Commun. Math. Phys. 94 (1984), 155-175. | MR 761792 | Zbl 0548.53054

[3] R. Bartnik, Results and conjectures in Mathematical Relativity, Proc. Geometry and Physics, Australian Nat. Univ. 22, 1989. | MR 1027863 | Zbl 0684.53052

[4] L. Bel, Introduction d'un tenseur du quatrième ordre, C.R. Acad. Sci. Paris 248 (1959), 1094-1096. | Zbl 0082.41204

[5] G. D. Birkhoff, Relativity and Modern Physics, Harvard Univ. Press, Cambridge, 1923. | JFM 49.0619.01

[6] H. Bondi, M. G. J. Van Der Burg, A. W. K. Metzner, Gravitational waves in General Relativity, VII, Proc. Roy. Soc. London 269 (1962), 21-52. | MR 147276 | Zbl 0106.41903

[7] J. P. Bourguignon, Les variétés de dimension quatre à courbure harmonique et à signature non nulle sont d'Einstein, Inventiones Math. 63 (1981), 263-286. | MR 610539 | Zbl 0456.53033

[8] J. P. Bourguignon, L'équation de la chaleur associée à la courbure de Ricci, Séminaire Bourbaki, Exposé n° 653, Astérisque 145-146 (1987), 45-61. | Numdam | MR 880025 | Zbl 0613.53018

[9] J. P. Bourguignon, P. Gauduchon, Spineurs, opérateurs de Dirac et variations de métriques, à paraître. | Zbl 0755.53009

[10] J. P. Bourguignon, H. Karcher, Curvature operators : pinching estimates and geometric examples, Ann. Sci. Ecole Norm. Sup. Paris 11 (1978), 71-92. | Numdam | MR 493867 | Zbl 0386.53031

[11] Y. Choquet-Bruhat, Théorème d'existence pour certains systè- mes d'équations aux dérivées partielles non-linéaires, Acta Math. 88 (1952), 141-225. | MR 53338 | Zbl 0049.19201

[12] Y. Choquet-Bruhat, Un théorème d'instabilité pour certaines équations hyperboliques non-linéaires, C.R. Acad. Sci. Paris 276, 281-284. | MR 315300 | Zbl 0245.35058

[13] D. Christodoulou, The nonlinear nature of Gravitation and gravitational wave experiments, Preprint, Courant Institute (1990). | MR 1123900

[14] D. Christodoulou, S. Klainerman, Asymptotic properties of linear field equations in Minkowski space, Commun. Pure Appl. Math. 43 (1990), 137-199. | MR 1038141 | Zbl 0715.35076

[15] D. Christodoulou, S. Klainerman, The global nonlinear stability of the Minkowski space, à paraître. | Numdam | Zbl 0733.35105

[16] A. H. Cook, Experiments on gravitation, in 300 years of gravitation, S.W. Hawking et W. Israel ed., Cambridge Univ. Press, Cambridge, (1987), 51-79. | MR 920449 | Zbl 0966.83506

[17] A. Einstein, Die Grundlage der allgemeinen Relativitätstheorie, Ann. Phys. 49 (1916), 769-822. | JFM 46.1293.01

[18] A. Einstein, M. Grossmann, Entwurf einer allgemeinerten Relativitätstheorie und einer Theorie der Gravitation, Z. Math. Phys. 62 (1913), I. Physikalischer Teil 225-244 ; II. Mathematischer Teil, 244-261. | JFM 45.1114.02

[19] A. Fischer, J. E. Marsden, The Einstein equations of evolution : a geometric approach, J. Math. Phys. 13 (1972), 546-568. | MR 299165 | Zbl 0233.58009

[20] A. Fischer, J. E. Marsden, The Einstein evolution equations as a first-order symmetric hyperbolic quasilinear system, Commun. Math. Phys. 28 (1972), 1-38. | MR 309507 | Zbl 0247.35082

[21] R. P. Geroch, What is a singularity in General Relativity ?, Ann. Phys. 48 (1968), 526-540. | Zbl 0167.56501

[22] S. W. Hawking, G. F. R. Ellis, The large scale structure of spacetime, Cambridge Monographs on Math. Phys., Cambridge, 1973. | Zbl 0265.53054

[23] S. W. Hawking, R. Penrose, The singularities of gravitational collapse and cosmology, Proc. Roy. Soc. London 314 (1970), 529- 548. | MR 264959 | Zbl 0954.83012

[24] D. Hilbert, Die Grundlagen der Physik, (Erste Mitteilung), Nachr. Gesellsch. Wiss. Göttingen 3 (1915), 395-407. | JFM 45.1111.01

[25] W. Israel, Dark stars : the evolution of an idea, in 300 years of gravitation, S.W. Hawking et W. Israel ed., Cambridge Univ. Press, Cambridge, (1987), 199-276. | MR 920452 | Zbl 0966.83504

[26] J. L. Kazdan, Positive energy in General Relativity, Séminaire Bourbaki, Exposé n° 593, Astérisque 92-93 (1982), 315-330. | Numdam | MR 689537 | Zbl 0496.53043

[27] S. Klainerman, The null condition and global existence to nonlinear wave equations, Lect. Appl. Math. 23 (1986), 293-326. | MR 837683 | Zbl 0599.35105

[28] M. D. Kruskal, Maximal extension of the Schwarzschild metric, Phys. Rev. 119 (1960), 1743-1745. | MR 115757 | Zbl 0098.19001

[29] J. Leray, Hyperbolic differential equations, notes Inst. Adv. Stud., Princeton (1952). | MR 80849

[30] A. Lichnerowicz, Sur certains problèmes globaux relatifs au systè- me des équations d'Einstein, Act. Sci. Ind. 833 (1939), Hermann, Paris. | JFM 65.1046.04 | Zbl 0061.47002

[31] H. A. Lorentz, Electromagnetic phenomena in a system moving with any velocity less than that of light, Proc. Acad. Sci. Amsterdam 6 (1904).

[32] H. Minkowski, Space and Time, Address at the 80th Assembly of German Natural Scientists and Physicians, Cologne (1908), in The principle of relativity, Dover Pub. (1952), 73-91.

[33] H. Minkowski, Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern, Nachr. Gesellsch. Wissensch., Göttingen (1908), 53. | JFM 39.0909.02

[34] C. Misner, K. Thorne, J. A. Wheeler, Gravitation, Freeman, San Francisco, 1973. | MR 418833

[35] C. Morawetz, The limiting amplitude principle, Commun. Pure Appl. Math. 15 (1962), 349-362. | MR 151712 | Zbl 0196.41202

[36] T. Parker, C. Taubes, On the proof by E. Witten of the positive mass conjecture, Commun. Math. Phys. 84 (1982), 223-238. | MR 661134 | Zbl 0528.58040

[37] R. Penrose, Unsolved problems in General Relativity, in Seminar in Differential Geometry, Ann. Math. Studies 102 (1981), 631-668. | MR 645761 | Zbl 0481.53053

[38] H. Poincaré, Sur la dynamique de l'électron, Rend. Circ. Mat. Palermo 21 (1906), 129-176. | JFM 37.0886.01

[39] R. K. Sachs, H. Wu, General Relativity for the mathematician, Grad. Texts in Math. 48, Springer Verlag, New York, 1977. | MR 503498 | Zbl 0373.53001

[40] R. Schoen, S. T. Yau, On the proof of the positive mass conjecture I, Commun. Math. Phys. 65 (1978), 45-76. | MR 526976 | Zbl 0405.53045

[41] R. Schoen, S. T. Yau, On the proof of the positive mass conjecture II, Commun. Math. Phys. 79 (1981), 231-260. | MR 612249 | Zbl 0494.53028

[42] K. Schwarzschild, Über das Gravitationsfeld eines Masses nach der Einsteinschen Theorie, Sitzungsber. Kônigl. Preuβ. Akad. Wiss. (1916), 189-196. | JFM 46.1296.02

[43] K. S. Thorne, Gravitational radiation, in 300 years of gravitation, S.W. Hawking et W. Israel ed., Cambridge Univ. Press, Cambridge, (1987), 330-458. | MR 920454 | Zbl 0966.83515

[44] H. Weyl, Raum, Zeit, Materie, (1920) ; Space, Time, Matter, Engl. version, Dover, New York, (1952). | Zbl 0186.28602

[45] E. Witten, A new proof of the positive energy theorem, Commun. Math. Phys 80 (1981), 381-402. | MR 626707 | Zbl 1051.83532

[46] S. T. Yau, Problems Section, in Seminar in Differential Geometry, Ann. Math. Studies 102 (1981), 695-697. | Zbl 0479.53001