The Q-curvature equation in conformal geometry
Géométrie différentielle, physique mathématique, mathématiques et société (II) - Volume en l'honneur de Jean-Pierre Bourguignon, Astérisque, no. 322 (2008), p. 23-38
@incollection{AST_2008__322__23_0,
     author = {Chang, Sun-Yung Alice and Yang, Paul C.},
     title = {The $Q$-curvature equation in conformal geometry},
     booktitle = {G\'eom\'etrie diff\'erentielle, physique math\'ematique, math\'ematiques et soci\'et\'e (II) - Volume en l'honneur de Jean-Pierre Bourguignon},
     editor = {Hijazi Oussama},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {322},
     year = {2008},
     pages = {23-38},
     zbl = {1182.53032},
     mrnumber = {2521652},
     language = {en},
     url = {http://www.numdam.org/item/AST_2008__322__23_0}
}
Chang, Sun-Yung Alice; Yang, Paul C. The $Q$-curvature equation in conformal geometry, in Géométrie différentielle, physique mathématique, mathématiques et société (II) - Volume en l'honneur de Jean-Pierre Bourguignon, Astérisque, no. 322 (2008), pp. 23-38. http://www.numdam.org/item/AST_2008__322__23_0/

[1] Adimurthi, F. Robert & M. Struwe - "Concentration phenomena for Liouville's equation in dimension four", J. Eur. Math. Soc. (JEMS) 8 (2006), p. 171-180. | MR 2239297 | Zbl 1387.35198

[2] S. Alexakis - "The decomposition of global conformal invariants: On a conjecture of Deser and Schwimmer", preprint arXiv:0711.1685. | Zbl 1258.53003

[3] M. T. Anderson - "L 2 curvature and volume renormalization of AHE metrics on 4-manifolds", Math. Res. Lett. 8 (2001), p. 171-188. | Article | MR 1825268 | Zbl 0999.53034

[4] M. Bonk, J. Heinonen & E. Saksman - "Logarithmic potentials, quasiconformal flows, and 𝒬-curvature", Duke Math. J. 142 (2008), p. 197-239. | Article | MR 2401620 | Zbl 1146.30010

[5] M. Bonk & U. Lang - "Bi-Lipschitz parameterization of surfaces", Math. Ann. 327 (2003), p. 135-169. | Article | MR 2006006 | Zbl 1042.53044

[6] T. P. Branson - "Differential operators canonically associated to a conformal structure", Math. Scand. 57 (1985), p. 293-345. | Article | MR 832360 | Zbl 0596.53009

[7] T. P. Branson, The functional determinant, Lecture Notes Series, vol. 4, Seoul National University Research, Institute of Mathematics Global Analysis Research Center, 1993. | MR 1325463 | Zbl 0827.58057

[8] T. P. Branson & B. Ørsted - "Explicit functional determinants in four dimensions", Proc. Amer. Math. Soc. 113 (1991), p. 669-682. | Article | MR 1050018 | Zbl 0762.47019

[9] S.-Y. A. Chang & J. Qing - "The zeta functional determinants on manifolds with boundary. I. The formula", J. Funct. Anal. 147 (1997), p. 327-362. | Article | MR 1454485 | Zbl 0914.58039

[10] S.-Y. A. Chang, J. Qing & P. C. Yang - "Compactification of a class of conformally flat 4-manifold", Invent. Math. 142 (2000), p. 65-93. | Article | MR 1784799 | Zbl 0990.53026

[11] S.-Y. A. Chang, J. Qing & P. C. Yang, "On the topology of conformally compact Einstein 4-manifolds", in Noncompact problems at the intersection of geometry, analysis, and topology, Contemp. Math., vol. 350, Amer. Math. Soc., 2004, p. 49-61. | Article | MR 2082390 | Zbl 1078.53031

[12] S.-Y. A. Chang, J. Qing & P. C. Yang, "On renormalized volume on conformally compact Einstein manifolds", in Proceedings DFDE-2005, Contemporary Mathematics, Fundamental Directions, 2005 (Russian).

[13] Z. Djadli & A. Malchiodi - "Existence of conformal metrics with constant 𝒬-curvature", preprint arXiv:math/0410141, to appear in Annals of Math.. | MR 2456884 | Zbl 1186.53050

[14] C. Fefferman & C. R. Graham - "Conformal invariants", Astérisque numéro hors série "The mathematical heritage of Élie Cartan (Lyon, 1984)" (1985), p. 95-116. | Numdam | MR 837196 | Zbl 0602.53007

[15] C. Fefferman & C. R. Graham, "𝒬-curvature and Poincaré metrics", Math. Res. Lett. 9 (2002), p. 139-151. | Article | MR 1909634 | Zbl 1016.53031

[16] C. Fefferman & C. R. Graham, "The ambient metric", preprint, 2007. | MR 2858236 | Zbl 1243.53004

[17] C. R. Graham - "Volume and area renormalizations for conformally compact Einstein metrics", in The Proceedings of the 19th Winter School "Geometry and Physics" (Srní, 1999), vol. 63, 2000, p. 31-42. | MR 1758076 | Zbl 0984.53020

[18] C. R. Graham, R. Jenne, L. J. Mason & G. A. J. Sparling - "Conformally invariant powers of the Laplacian. I. Existence", J. London Math. Soc. 46 (1992), p. 557-565. | Article | MR 1190438 | Zbl 0726.53010

[19] C. R. Graham & A. Juhl - "Holographic formula for 𝒬-curvature", preprint, to appear in Advances in Math., 2006. | MR 2351380 | Zbl 1147.53030

[20] C. R. Graham & M. Zworski - "Scattering matrix in conformal geometry", Invent. Math. 152 (2003), p. 89-118. | Article | MR 1965361 | Zbl 1030.58022

[21] M. J. Gursky & J. A. Vlaclovsky - "A fully nonlinear equation on four-manifolds with positive scalar curvature", J. Differential Geom. 63 (2003), p. 131-154. | Article | MR 2015262 | Zbl 1070.53018

[22] A. Huber - "On subharmonic functions and differential geometry in the large", Comment. Math. Helv. 32 (1957), p. 13-72. | Article | MR 94452 | Zbl 0080.15001

[23] S. Paneitz - "A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds", preprint, 1993. | MR 2393291 | Zbl 1145.53053

[24] S. J. Patterson & P. A. Perry - "The divisor of Selberg's zeta function for Kleinian groups", Duke Math. J. 106 (2001), p. 321-390. | Article | MR 1813434 | Zbl 1012.11083

[25] X. Xu - "Uniqueness theorem for integral equations and its application", J. Funct. Anal. 247 (2007), p. 95-109. | Article | MR 2319755 | Zbl 1153.45005