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://www.numdam.org/item/TSG_1997-1998__16__107_0/}
}
TY  - JOUR
AU  - Herzlich, Marc
TI  - Théorèmes de masse positive
JO  - Séminaire de théorie spectrale et géométrie
PY  - 1997-1998
SP  - 107
EP  - 126
VL  - 16
PB  - Institut Fourier
PP  - Grenoble
UR  - http://www.numdam.org/item/TSG_1997-1998__16__107_0/
LA  - fr
ID  - TSG_1997-1998__16__107_0
ER  - 
%0 Journal Article
%A Herzlich, Marc
%T Théorèmes de masse positive
%J Séminaire de théorie spectrale et géométrie
%D 1997-1998
%P 107-126
%V 16
%I Institut Fourier
%C Grenoble
%U http://www.numdam.org/item/TSG_1997-1998__16__107_0/
%G fr
%F TSG_1997-1998__16__107_0
Herzlich, Marc. Théorèmes de masse positive. Séminaire de théorie spectrale et géométrie, Tome 16 (1997-1998), pp. 107-126. http://www.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 | Zbl

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

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

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

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

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

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

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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

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

[20] G. Galloway, private communication.

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

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

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

[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 | Zbl

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

[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 | Zbl

[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

[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 | Zbl

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

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

[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 | Zbl

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

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

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

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

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

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

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

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

[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

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

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

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

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

[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 | Zbl

[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 | Zbl

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

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

[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 | Zbl

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

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

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