Compactification conforme des variétés asymptotiquement plates

 Access to full text

 Full (PDF)

1. [1] ANDERSON (M.T.). — Ricci curvature bounds and Einstein metrics on compact manifolds, J. Amer. Math. Soc., t. 2, 1989, p. 455-490. Zbl0694.53045MR90g:53052
2. [2] ANDERSSON (L.), CHRUŚCIEL (P.T.) and FRIEDRICH (H.). — On the regularity of solutions to the Yamabe equation and the existence of smooth hyperboidal initial data for Einstein's equations, Commun. Math. Phys., t. 149, 1992, p. 587-612. Zbl0764.53027
3. [3] ASHTEKAR (A.). — On the boundary conditions for gravitational and gauge fields aat spatial infinity, Asymptotic behaviour of mass and spacetime geometry, F.J. Flaherty, ed., Proceedings, Corvallis, Oregon, 1983, Lect. Notes in Physics, t. 202, Springer, 1984, p. 95-109. Zbl0553.53050
4. [4] ASHTEKAR (A.) and HANSEN (R.O.). — A unified treatment of null and spatial infinity in general relativity, J. Math. Phys., t. 19, 1978, p. 1542-1566. MR58 #20188
5. [5] ASHTEKAR (A.) and MAGNON (A.). — From i0 to the 3 + 1 description of infinity, J. Math. Phys., t. 25, 1984, p. 2682-2691. Zbl0559.53044MR85i:83017
6. [6] BANDO (S.), KASUE (A.), and NAKAJIMA (H.). — On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth, Invent. Math., t. 97, 1989, p. 313-349. Zbl0682.53045MR90c:53098
7. [7] BARTNIK (R.). — The mass of an asymptotically flat manifold. — Commun. Pure Appl. Math., t. 39, 1986, p. 661-693. Zbl0598.53045MR88b:58144
8. [8] BERS (L.), JOHN (F.) and SCHECHTER (M.). — Partial differential equations. — American Mathematical Society, Providence, 1974. 
9. [9] BESSE (A.L.). — Einstein manifolds, Ergeb. Math. Grenzgeb., t. 10, Springer, Berlin, 1987. Zbl0613.53001MR88f:53087
10. [10] CARTAN (É.). — Les espaces à connexion conforme, Ann. Soc. Pol. Mat., t. 22, 1923, p. 171-221. Zbl50.0493.01JFM50.0493.01
11. [11] FRIEDRICH (H.). — Cauchy problems for the conformal vacuum field equations in General Relativity, Commun. Math. Phys., t. 91, 1983, p. 445-472. Zbl0555.35116MR85g:83005
12. [12] FRIEDRICH (H.). — Einstein equations and conformal structure : existence of Anti-de Sitter-type spacetimes, J. Geom. Phys., t. 17, 1995, p. 125-184. Zbl0840.53055MR96j:83008
13. [13] GAUDUCHON (P.). — Connexion canonique et structures de Weyl en géométrie conforme, Juin 1990, non publié. 
14. [14] GREENE (R.), PETERSEN (P.) and ZHU (S.). — Riemannian manifolds of faster-than-quadratic curvature decay, Int. Math. Res. Notices, t. 9, 1994, p. 363-377. Zbl0833.53037MR95m:53054
15. [15] HAWKING (S.W.) and ELLIS (G.F.R.). — The large-scale structure of space-time. — Cambridge Univ. Press, Cambridge, 1973. Zbl0265.53054MR54 #12154
16. [16] HEBEY (E.) and HERZLICH (M.). — Convergence of riemannian manifolds; a status report, Preprint École Polytechnique (Palaiseau), n° 1096, 1995. 
17. [17] LEE (J.) and PARKER (T.H.). — The Yamabe problem, Bull. Amer. Math. Soc., t. 117, 1987, p. 37-91. Zbl0633.53062MR88f:53001
18. [18] LOCKHART (R.B.). — Fredholm properties of a class of elliptic operators on non-compact manifolds, Duke Math. J., t. 48, 1983, p. 289-312. Zbl0486.35027MR82j:35050
19. [19] LOCKHART (R.B.) and MCOWEN (R.). — Elliptic differential operators on non-compact manifolds, Ann. Scuola. Norm. Sup. Pisa, t. 12, 1985, p. 409-447. Zbl0615.58048MR87k:58266
20. [20] MAZ'YA (V.G.) and PLAMENEEVSKI (B.A.). — Estimates in Lp and in Hölder classes and the Miranda-Agmon Maximum principle for solutions of elliptic boundary value problems in domains with singular points on the boundary (en russe), Math. Nachr., t. 81, 1978, p. 25-82; trad. anglaise Amer. Math. Soc. Transl., t. 123, 1984, p. 1-56. Zbl0554.35035
21. [21] PENROSE (R.). — Conformal treatment of infinity, Relativity, groups and topology (C. de Witt and B. de Witt, eds.), École d'été de Physique Théorique, Les Houches 1963. — Gordon and Breach, 1963. 
22. [22] SCHOEN (R.). — Conformal deformation of a Riemannian manifold to constant scalar curvature, J. Diff. Geom, t. 20, 1984, p. 479-495. Zbl0576.53028MR86i:58137
23. [23] WEYL (H.). — Zur Infinitesimalgeometrie : Einordnung der projektiven und den konform Auffassung, Göttinger Nachrichten, 1921, p. 99-112, repris dans Gesammelte Abhandlungen, vol. II, Chelsea, New York, 1967, p. 195-207. Zbl48.0844.04JFM48.0844.04

1. Marc Herzlich, L'inégalité de Penrose