Stabilité par déformation non-linéaire de la métrique de Minkowski

Jean-Pierre Bourguignon

Séminaire Bourbaki (1990-1991)

  • Volume: 33, page 321-358
  • ISSN: 0303-1179

How to cite

top

Bourguignon, Jean-Pierre. "Stabilité par déformation non-linéaire de la métrique de Minkowski." Séminaire Bourbaki 33 (1990-1991): 321-358. <http://eudml.org/doc/110142>.

@article{Bourguignon1990-1991,
author = {Bourguignon, Jean-Pierre},
journal = {Séminaire Bourbaki},
keywords = {Schwarzschild metric; conformal geometry},
language = {fre},
pages = {321-358},
publisher = {Société Mathématique de France},
title = {Stabilité par déformation non-linéaire de la métrique de Minkowski},
url = {http://eudml.org/doc/110142},
volume = {33},
year = {1990-1991},
}

TY - JOUR
AU - Bourguignon, Jean-Pierre
TI - Stabilité par déformation non-linéaire de la métrique de Minkowski
JO - Séminaire Bourbaki
PY - 1990-1991
PB - Société Mathématique de France
VL - 33
SP - 321
EP - 358
LA - fre
KW - Schwarzschild metric; conformal geometry
UR - http://eudml.org/doc/110142
ER -

References

top
  1. [1] R. Arnowitt, S. Deser, C. Misner, Coordinate invariance and energy expressions in General Relativity, Phys. Rev.122 (1961), 997-1006. Zbl0094.23003MR127946
  2. [2] R. Bartnik, Existence of maximal surfaces in asymptotically flat space-times, Commun. Math. Phys.94 (1984), 155-175. Zbl0548.53054MR761792
  3. [3] R. Bartnik, Results and conjectures in Mathematical Relativity, Proc. Geometry and Physics, Australian Nat. Univ.22, 1989. Zbl0684.53052MR1027863
  4. [4] L. Bel, Introduction d'un tenseur du quatrième ordre, C.R. Acad. Sci. Paris248 (1959), 1094-1096. Zbl0082.41204
  5. [5] G.D. Birkhoff, Relativity and Modern Physics, Harvard Univ. Press, Cambridge, 1923. Zbl49.0619.01JFM49.0619.01
  6. [6] H. Bondi, M.G.J. Van Der Burg, A.W.K. Metzner, Gravi- tational waves in General Relativity, VII, Proc. Roy. Soc. London269 (1962), 21-52. Zbl0106.41903MR147276
  7. [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. Zbl0456.53033MR610539
  8. [8] J.P. Bourguignon, L'équation de la chaleur associée à la courbure de Ricci, Séminaire Bourbaki, Exposé n° 653, Astérisque145-146 (1987), 45-61. Zbl0613.53018MR880025
  9. [9] J.P. Bourguignon, P. Gauduchon, Spineurs, opérateurs de Dirac et variations de métriques, à paraître. Zbl0755.53009
  10. [10] J.P. Bourguignon, H. Karcher, Curvature operators : pinching estimates and geometric examples, Ann. Sci. Ecole Norm. Sup.Paris11 (1978), 71-92. Zbl0386.53031MR493867
  11. [11] Y. Choquet-Bruhat, Théorème d'existence pour certains systè- mes d'équations aux dérivées partielles non-linéaires, Acta Math.88 (1952), 141-225. Zbl0049.19201MR53338
  12. [12] Y. Choquet-Bruhat, Un théorème d'instabilité pour certaines équations hyperboliques non-linéaires, C.R. Acad. Sci. Paris276, 281-284. Zbl0245.35058MR315300
  13. [13] D. Christodoulou, The nonlinear nature of Gravitation and gravitational wave experiments, Preprint, Courant Institute (1990). Zbl0990.83504MR1123900
  14. [14] D. Christodoulou, S. Klainerman, Asymptotic properties of linear field equations in Minkowski space, Commun. Pure Appl. Math.43 (1990), 137-199. Zbl0715.35076MR1038141
  15. [15] D. Christodoulou, S. Klainerman, The global nonlinear stability of the Minkowski space, à paraître. Zbl0733.35105
  16. [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. Zbl0966.83506MR920449
  17. [17] A. Einstein, Die Grundlage der allgemeinen Relativitätstheorie, Ann. Phys.49 (1916), 769-822. Zbl46.1293.01JFM46.1293.01
  18. [18] A. Einstein, M. Grossmann, Entwurf einer allgemeinerten Relativitätstheorie und einer Theorie der Gravitation, Z. Math. Phys.62 (1913), I. Physikalischer Teil225-244 ; II. Mathematischer Teil, 244-261. Zbl45.1114.02JFM45.1114.02
  19. [19] A. Fischer, J.E. Marsden, The Einstein equations of evolution : a geometric approach, J. Math. Phys.13 (1972), 546-568. Zbl0233.58009MR299165
  20. [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. Zbl0247.35082MR309507
  21. [21] R.P. Geroch, What is a singularity in General Relativity ?, Ann. Phys.48 (1968), 526-540. Zbl0167.56501
  22. [22] S.W. Hawking, G.F.R. Ellis, The large scale structure of spacetime, Cambridge Monographs on Math. Phys., Cambridge, 1973. Zbl0265.53054
  23. [23] S.W. Hawking, R. Penrose, The singularities of gravitational collapse and cosmology, Proc. Roy. Soc. London314 (1970), 529- 548. Zbl0954.83012MR264959
  24. [24] D. Hilbert, Die Grundlagen der Physik, (Erste Mitteilung), Nachr. Gesellsch. Wiss. Göttingen3 (1915), 395-407. Zbl45.1111.01JFM45.1111.01
  25. [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. Zbl0966.83504MR920452
  26. [26] J.L. Kazdan, Positive energy in General Relativity, Séminaire Bourbaki, Exposé n° 593, Astérisque92-93 (1982), 315-330. Zbl0496.53043MR689537
  27. [27] S. Klainerman, The null condition and global existence to nonlinear wave equations, Lect. Appl. Math.23 (1986), 293-326. Zbl0599.35105MR837683
  28. [28] M.D. Kruskal, Maximal extension of the Schwarzschild metric, Phys. Rev.119 (1960), 1743-1745. Zbl0098.19001MR115757
  29. [29] J. Leray, Hyperbolic differential equations, notes Inst. Adv. Stud., Princeton (1952). MR80849
  30. [30] A. Lichnerowicz, Sur certains problèmes globaux relatifs au systè- me des équations d'Einstein, Act. Sci. Ind.833 (1939), Hermann, Paris. Zbl0061.47002JFM65.1046.04
  31. [31] H.A. Lorentz, Electromagnetic phenomena in a system moving with any velocity less than that of light, Proc. Acad. Sci. Amsterdam6 (1904). 
  32. [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. [33] H. Minkowski, Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern, Nachr. Gesellsch. Wissensch., Göttingen (1908), 53. Zbl39.0909.02JFM39.0909.02
  34. [34] C. Misner, K. Thorne, J.A. Wheeler, Gravitation, Freeman, San Francisco, 1973. MR418833
  35. [35] C. Morawetz, The limiting amplitude principle, Commun. Pure Appl. Math.15 (1962), 349-362. Zbl0196.41202MR151712
  36. [36] T. Parker, C. Taubes, On the proof by E. Witten of the positive mass conjecture, Commun. Math. Phys.84 (1982), 223-238. Zbl0528.58040MR661134
  37. [37] R. Penrose, Unsolved problems in General Relativity, in Seminar in Differential Geometry, Ann. Math. Studies102 (1981), 631-668. Zbl0481.53053MR645761
  38. [38] H. Poincaré, Sur la dynamique de l'électron, Rend. Circ. Mat. Palermo21 (1906), 129-176. Zbl37.0886.01JFM37.0886.01
  39. [39] R.K. Sachs, H. Wu, General Relativity for the mathematician, Grad. Texts in Math.48, Springer Verlag, New York, 1977. Zbl0373.53001MR503498
  40. [40] R. Schoen, S.T. Yau, On the proof of the positive mass conjecture I, Commun. Math. Phys.65 (1978), 45-76. Zbl0405.53045MR526976
  41. [41] R. Schoen, S.T. Yau, On the proof of the positive mass conjecture II, Commun. Math. Phys.79 (1981), 231-260. Zbl0494.53028MR612249
  42. [42] K. Schwarzschild, Über das Gravitationsfeld eines Masses nach der Einsteinschen Theorie, Sitzungsber. Kônigl. Preuβ. Akad. Wiss. (1916), 189-196. Zbl46.1296.02JFM46.1296.02
  43. [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. Zbl0966.83515MR920454
  44. [44] H. Weyl, Raum, Zeit, Materie, (1920) ; Space, Time, Matter, Engl. version, Dover, New York, (1952). Zbl0186.28602
  45. [45] E. Witten, A new proof of the positive energy theorem, Commun. Math. Phys80 (1981), 381-402. Zbl1051.83532MR626707
  46. [46] S.T. Yau, Problems Section, in Seminar in Differential Geometry, Ann. Math. Studies102 (1981), 695-697. Zbl0479.53001

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.