Théorèmes de masse positive
Séminaire de théorie spectrale et géométrie, Tome 16 (1997-1998), pp. 107-126.
@article{TSG_1997-1998__16__107_0,
     author = {Herzlich, Marc},
     title = {Th\'eor\`emes de masse positive},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {107--126},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {16},
     year = {1997-1998},
     zbl = {0949.53002},
     language = {fr},
     url = {http://archive.numdam.org/item/TSG_1997-1998__16__107_0/}
}
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Herzlich, Marc. Théorèmes de masse positive. Séminaire de théorie spectrale et géométrie, Tome 16 (1997-1998), pp. 107-126. http://archive.numdam.org/item/TSG_1997-1998__16__107_0/

[1] L. Andersson and M. Dahl, Scalar curvature rigidity for asymptotically locally hyperbolic manifolds, Ann. Glob. Anal. Geom. 16 ( 1998), 1-27. | MR 1616570 | Zbl 0946.53021

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

[3] T. Aubin, Équations différentielles non -linéaires et problème de Yamabe concernant la courbure scalaire, J. Math. Pures Appl. 55 ( 1976), 269-296. | MR 431287 | Zbl 0336.53033

[4] P. Aviles and R. Mcowen, Conformat deformation of complete manifolds with negative curvature, J. Diff. Geom. 21 ( 1985), 269-281. | MR 816672 | Zbl 0588.53028

[5] P. Aviles and R. Mcowen, Conformal deformation to constant negative scalar curvature on noncompact riemannian manifolds, J. Diff. Geom. 27 ( 1988), 225-239. | MR 925121 | Zbl 0648.53021

[6] A. Bahri and H. Brezis, Équations elliptiques non-linéaires sur des variétés avec exposant de Sobolev critique, C.R. Acad. Sci. Paris 307 ( 1988), 573-576. | MR 967364 | Zbl 0694.35059

[7] C. Bandle, Isoperimetric inequalities, Pitman, London, 1980.

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

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

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

[11] R. Bartnik, New definition of quasi-local mass, Phys. Rev. Lett. 62 ( 1989), 2346-2348. | MR 996396

[12] O. Biquard, Métriques d'Einstein asymptotiquemen t symétriques, École Polytechnique ( 1997), preprint. | MR 1468928

[13] O. Biquard, Einstein deformations of hyperbolic metrics, École Polytechnique ( 1998), preprint. | MR 1798612

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

[15] H. Bray, Ph. D thesis, Stanford University, 1997.

[16] M. Dahl, The positive mass argument for ALE and ALH manifolds, Mathematics of Gravitation, Banach Center Publ., vol. 41, 1997, pp. 133-142. | MR 1466513 | Zbl 0890.53065

[17] E. Delay, Analyse précisée d'équations semi- linéaires elliptiques sur l'espace hyperbolique et application à la courbure scalaire conforme, Bull. Soc. Math. Fr. 125 ( 1997), 345-381. | Numdam | MR 1605461 | Zbl 0939.53026

[18] V. Denisov and 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), 832-838, english translation. | Zbl 0541.53024

[19] J. Escobar, The geometry of the first non-zero Stekloff eigenvalue, J. Funct. Anal. 150 ( 1997), 544-556. | MR 1479552 | Zbl 0888.58066

[20] G. Galloway, private communication.

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

[22] R. Geroch, General relativity, in Differential geometry, Proc. Symp. Pure Math., vol. 27, Amer. Math. Soc, 1975. | MR 378703 | Zbl 0307.53038

[23] C. R. Graham and J. Lee, Einstein metrics with prescribed conformal infinity on the ball, Adv. Math. 87 ( 1991), 186-225. | MR 1112625 | Zbl 0765.53034

[24] R. Greene, P. Petersen and S. Zhu, Riemannian manifolds of faster- than-quadratic curvature decay, Int. Math. Res. Notices 9 ( 1994), 363-377. | MR 1301436 | Zbl 0833.53037

[25] L. Habermann and J. Jost, Green functions and conformal geometry, I and II MPI Leipzig ( 1997), preprint. | MR 1806066

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

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

[28] M. Herzlich, Minimal surfaces, the Dirac operator and the Penrose inequality. Actes de la table ronde A.L. Besse de géométrie pseudoriemannienne, Nancy, 1-6 Juin 1998, to appear. | Numdam | MR 1987634

[29] M. Herzlich, Métriques privilégiées dans la classe conforme d'une variété asymptotiquement plate, et applications, C.R. Acad. Sci. Paris 323 ( 1996), 287-292. | MR 1404775 | Zbl 0861.53037

[30] M. Herzlich, A Penrose-like inequality for the mass of Riemannian asymptotically flat manifolds, Commun. Math. Phys. 188 ( 1997), 121-133. | MR 1471334 | Zbl 0886.53032

[31] M. Herzlich, Scalar curvature and rigidity for odd-dimensional complex hyperbolic spaces, Math. Annalen ( 1998), to appear. | MR 1660251 | Zbl 0946.53022

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

[33] G. Huisken and T. Ilmanen, The Riemannian Penrose inequality, Int. Math. Res. Not. 20 ( 1997), 1045-1058. | MR 1486695 | Zbl 0905.53043

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

[35] A. Kasue, A compactification of a manifold with asymptotically nonnegative curvature, Ann. Scient. Ec. Norm. Sup. Paris 21 ( 1988), 593-622. | Numdam | MR 982335 | Zbl 0662.53032

[36] J. Kazdan, Positive energy in general relativity, Sém. Bourbaki n° 593, Astérisque, vol. 92-93, Soc. math. France, 1982. | Numdam | MR 689537 | Zbl 0496.53043

[37] P.B. Kronheimer, A Torelli type theorem for gravitational instantons, J. Diff. Geom. 29 ( 1989), 685-697. | MR 992335 | Zbl 0671.53046

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

[39] M.C. Leung, Pinching theorem on asymptotically hyperbolic spaces, Int. J. Math. 5 ( 1993), 841-857. | MR 1245353 | Zbl 0810.53032

[40] A. Lichnerowicz, Spineurs harmoniques, C.R. Acad. Sci. Paris 257 ( 1963), 7-9. | MR 156292 | Zbl 0136.18401

[41] E. Malec and K. Roszkowski, Comment on Herzlich's proof of the Penrose inequality, Jagiellon Univ, Krakow ( 1998), preprint, g r - qc 9806035. | MR 1652117

[42] M. Min-Oo, Scalar curvature rigidity of asymptotically hyperbolic spin manifolds, Math. Ann. 285 ( 1989), 527-539. | MR 1027758 | Zbl 0686.53038

[43] R. Penrose, Naked singularities, Ann. N. Y.Acad. Sci. 224 ( 1973), 125-134. | Zbl 0925.53023

[44] Oo. Reula and K.P. Tod, Positivity of the Bondi energy, J. Math. Phys. 25 ( 1984), 1004-1008. | MR 739255

[45] R. Schoen, Conformal deformation of a Riemannian manifold to constant scalar curvature, J. Diff. Geom 20 ( 1984), 479-495. | MR 788292 | Zbl 0576.53028

[46] R. Schoen, Variational theory for the total scalar curvature functional for Riemannian metrics and related topics, Topics in Calculus of Variations (M. Giaquinta, ed.), Lect. Notes in Math., vol. 1365, Springer, 1989, pp. 121-154. | MR 994021 | Zbl 0702.49038

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

[48] R. Schoen and S. T. Yau, On the structure of manifolds with positive scalar curvature, Manuscripta math. 28 ( 1979), 159-183. | MR 535700 | Zbl 0423.53032

[49] R. Schoen and S. T. Yau, Conformally flat manifolds, Kleinian groups and scalar curvature, Invent. Math. 92 ( 1988), 47-71. | MR 931204 | Zbl 0658.53038

[50] K. S. Thorne, Magic without magic, Freeman, San Francisco, 1972.

[51] P. Tod, private communication.

[52] N. Trudinger, Remarks concerning the conformal deformation of Riemannian structures on compact manifolds, Ann. Scuola Norm. Sup. Pisa 22 ( 1968), 265-274. | Numdam | MR 240748 | Zbl 0159.23801

[53] S. Unnebrink, Asymptotically flat four-manifolds, Diff. Geom. Appl. 6 ( 1996), 271-274. | MR 1408311 | Zbl 0856.53031

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

[55] H. Yamabe, On a deformation of Riemannian structures on compact manifolds, Osaka Math. J. 12 ( 1960), 21-37. | MR 125546 | Zbl 0096.37201