L'inégalité de Penrose
Séminaire Bourbaki : volume 2000/2001, exposés 880-893, Astérisque no. 282  (2002), Talk no. 883, p. 85-111
@incollection{SB_2000-2001__43__85_0,
     author = {Herzlich, Marc},
     title = {L'in\'egalit\'e de Penrose},
     booktitle = {S\'eminaire Bourbaki : volume 2000/2001, expos\'es 880-893},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {282},
     year = {2002},
     note = {talk:883},
     pages = {85-111},
     zbl = {1042.53022},
     mrnumber = {1975176},
     language = {fr},
     url = {http://www.numdam.org/item/SB_2000-2001__43__85_0}
}
Herzlich, Marc. L'inégalité de Penrose, in Séminaire Bourbaki : volume 2000/2001, exposés 880-893, Astérisque, no. 282 (2002), Talk no. 883, pp. 85-111. http://www.numdam.org/item/SB_2000-2001__43__85_0/

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

[2] S. Bando, A. Kasue & H. Nakajima - « On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth », Invent. math. 97 (1989), p. 313-349. | MR 1001844 | Zbl 0682.53045

[3] C. Bär - « Lower eigenvalues estimates for Dirac operators », Math. Ann. 293 (1992), p. 39-46. | MR 1162671 | Zbl 0741.58046

[4] R. Bartnik - « The mass of an asymptotically flat manifold », Commun. Pure. Appl. Math. 39 (1986), p. 661-693. | MR 849427 | Zbl 0598.53045

[5] _, « New definition of quasi-local mass », Phys. Rev. Lett. 62 (1989), p. 2346-2348. | MR 996396

[6] _, « Quasi-spherical metrics and prescribed scalar curvature », J. Diff. Geom. 37 (1993), p. 31-71. | MR 1198599 | Zbl 0786.53019

[7] R. Bishop & R. Crittenden - Geometry of manifolds, Pure Appl. Math., vol. XV, Acad. Press, New York, 1964. | MR 169148 | Zbl 0132.16003

[8] J.-P. Bourguignon - « Stabilité par déformation non-linéaire de la métrique de Minkowski », Sém. Bourbaki n° 740, Astérisque, vol. 201-202-203, Soc. math. France, 1991, p. 321-358. | Numdam | MR 1157847 | Zbl 0754.53060

[9] H. Bray - « Proof of the Riemannian Penrose conjecture using the positive mass theorem », J. Diff. Geom., 59 (2001), p. 177-267. | MR 1908823 | Zbl 1039.53034

[10] H. Bray & F. Finster - « Curvature estimates and the positive mass theorem », Commun. Anal. Geom., 10 (2002), p. 291-306. | MR 1900753 | Zbl 1030.53041

[11] H. Bray & R. Schoen - « Recent proofs of the Riemannian Penrose inequality », Current Developments in Mathematics, Harvard Univ., 1999. | MR 1990246

[12] G. L. Bunting &, A. K. Masood-Ul-Alam - « Non-existence of multiple black holes in asymptotically euclidean vacuum spacetimes », Gen. Rel. Grav. 19 (1987), p. 147-154. | MR 876598 | Zbl 0615.53055

[13] Y. Choquet-Bruhat - « Positive energy theorems », Relativity, groups and topology II, Les Houches XL, 1983 (B. De Witt & R. Stora, éds.), Elsevier, Amsterdam, 1984, p. 740-785. | MR 830248 | Zbl 0593.53055

[14] P. T. Chruściel - « Boundary conditions at spatial infinity from a Hamiltonian point of view », Topological properties and global structure of spacetime, Erice 1985 (P. Bergmann & V. de Sabbata, éds.), Plenum, New York, 1986, p. 49-59. | MR 1102938 | Zbl 0687.53070

[15] _, « On the invariant mass conjecture in General Relativity », Commun. Math. Phys 120 (1988), p. 233-248. | MR 973533 | Zbl 0661.53060

[16] V. Denisov & O. Solovev - « The energy determined in General Relativity on the basis of the traditional Hamiltonian approach does not have physical meaning », Theor. Math. Phys. 56 (1983), p. 832-838, english translation. | Zbl 0541.53024

[17] L. C. Evans & J. Spruck - « Motion of level sets by mean curvature », J. Diff. Geom. 33 (1991), p. 635-681. | MR 1100206 | Zbl 0726.53029

[18] R. Geroch - « Energy extraction », Ann. N. Y. Acad. Sci. 224 (1973), p. 108-117. | Zbl 0942.53509

[19] _, « General Relativity », in Differential geometry, Proc. Symp. Pure Math., vol. 27, Amer. Math. Soc., Providence, 1975. | MR 378703

[20] R. Hardt & X. Zhou - « An evolution problem for linear growth functionals », Comm. Partial Differential Equations 19 (1994), p. 1879-1907. | MR 1301176 | Zbl 0811.35061

[21] S. Hawking - « Gravitational radiation in an expanding universe », J. Math. Phys. 9 (1968), p. 598-604.

[22] S. W. Hawking & G. Ellis - The large-scale structure of space-time, Cambridge Univ. Press, Cambridge, 1973. | MR 424186 | Zbl 0265.53054

[23] M. Herzlich - « Compactification conforme des variétés asymptotiquement plates », Bull. Soc. math. France 125 (1997), p. 55-92. | Numdam | MR 1459298 | Zbl 0938.53020

[24] _, « A Penrose-like inequality for the mass of Riemannian asymptotically flat manifolds », Commun. Math. Phys. 188 (1997), p. 121-133. | MR 1471334 | Zbl 0886.53032

[25] O. Hijazi - « Première valeur propre de l'opérateur de Dirac et nombre de Yamabe », C. R. Acad. Sci. Paris 313 (1991), p. 865-868. | MR 1138566 | Zbl 0738.53030

[26] G. Huisken & T. Ilmanen - « The inverse mean curvature flow and the Riemannian Penrose inequality », J. Diff. Geom., 59 (2001), p. 353-437. | MR 1916951 | Zbl 1055.53052

[27] _, « Proof of the Penrose inequality », Int. Math. Res. Not. 20 (1997), p. 1045-1058, annonce. | Zbl 0905.53043

[28] T. Ilmanen - Elliptic regularization and partial regularity for motion by mean curvature, Memoirs Amer. Math. Soc., vol. 520, Amer. Math. Soc., Providence, RI, 1994. | MR 1196160 | Zbl 0798.35066

[29] P. S. Jang & R. Wald - « The positive energy conjecture and the cosmic censor hypothesis », J. Math. Phys. 18 (1977), p. 41-44. | MR 523907

[30] J. Kazdan - « Positive energy in General Relativity », Sém. Bourbaki n° 593, Astérisque, vol. 92-93, Soc. math. France, 1982, p. 315-330. | Numdam | MR 689537 | Zbl 0496.53043

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

[32] J. Lee & T. H. Parker - « The Yamabe problem », Bull. Amer. Math. Soc. 17 (1987), p. 37-91. | MR 888880 | Zbl 0633.53062

[33] A. Lichnerowicz - Théories relativistes de la gravitation et de l'électromagnétisme, Masson, Paris, 1955. | Zbl 0065.20704

[34] _, « Spineurs harmoniques », C. R. Acad. Sci. Paris 257 (1963), p. 7-9. | MR 156292 | Zbl 0136.18401

[35] A. Lichnewsky & R. Temam - « Pseudosolutions of the time-dependant minimal surface problem », J. Diff. Eq. 30 (1978), p. 340-363. | MR 521858 | Zbl 0368.49016

[36] R. B. Lockhart - « Fredholm properties of a class of elliptic operators on non-compact manifolds », Duke Math. J. 48 (1983), p. 289-312. | MR 610188 | Zbl 0486.35027

[37] R. B. Lockhart & R. Mcowen - « Elliptic differential operators on non-compact manifolds », Ann. Scuola. Norm. Sup. Pisa 12 (1985), p. 409-447. | Numdam | MR 837256 | Zbl 0615.58048

[38] S. Luckhaus - « Solutions for the two-phase Stefan problem with the Gibbs-Thompson law for the melting temperature », Eur. J. Appl. Math. 1 (1990), p. 101-111. | MR 1117346 | Zbl 0734.35159

[39] E. Malec & N. O'Murchadha - « Trapped surfaces and the Penrose inequality in spherically symmetric geometries », Phys. Rev. D 49 (1994), p. 6931-6934. | MR 1278625

[40] U. Massari & M. Miranda - Minimal surfaces of codimension one, North-Holland Math. Stud., vol. 91, Elsevier, 1984. | MR 795963 | Zbl 0565.49030

[41] B. O'Neill - Semi-Riemannian geometry, Acad. Press, San Diego, 1983. | MR 719023 | Zbl 0531.53051

[42] R. Penrose - « Conformal treatment of infinity », Relativity, groups and topology (C. de Witt & B. de Witt, éds.), École d'été de Physique Théorique, Les Houches 1963, Cordon and Breach, 1963, p. 563-584. | MR 168334 | Zbl 0148.46403

[43] _, « Naked singularities », Ann. N. Y. Acad. Sci. 224 (1973), p. 125-134.

[44] R. Schoen & S. T. Yau - « On the proof of the positive mass conjecture in General Relativity », Commun. Math. Phys 65 (1979), p. 45-76. | MR 526976 | Zbl 0405.53045

[45] _, « On the structure of manifolds with positive scalar curvature », Manuscripta math. 28 (1979), p. 159-183. | MR 535700 | Zbl 0423.53032

[46] _, « The energy and linear-momentum of spacetimes in general relativity », Commun. Math. Phys. 79 (1981), p. 47-51. | MR 609227 | Zbl 0934.83031

[47] K. Schwarzschild - « Über das Gravitationsfeld eines Masses nach der Einsteinschen Theorie », Sitz. König. Preuss. Akad. Wiss. (1916), p. 189-196. | JFM 46.1296.02

[48] L. Simon - Lectures on geometric measure theory, Proc. Centre Math. Anal., vol. 3, Austr. Nat. Univ., 1983. | MR 756417 | Zbl 0546.49019

[49] P. Sternberg, G. Williams & W. P. Ziemer - « Regularity of constrained area minimizing hypersurfaces », J. Diff. Eq. 94 (1991), p. 83-94. | MR 1133542 | Zbl 0743.49016

[50] A. Visintin - « Nucleation and mean curvature flow », Comm. Partial Differential Equations 23 (1998), p. 17-53. | MR 1608492 | Zbl 0901.53045

[51] R. Wald - General Relativity, Univ. Chicago Press, Chicago, 1984. | MR 757180 | Zbl 0549.53001

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