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), pp. 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},
     pages = {23--38},
     year = {2008},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {322},
     mrnumber = {2521652},
     zbl = {1182.53032},
     language = {en},
     url = {https://www.numdam.org/item/AST_2008__322__23_0/}
}
TY  - CHAP
AU  - Chang, Sun-Yung Alice
AU  - Yang, Paul C.
TI  - The $Q$-curvature equation in conformal geometry
BT  - Géométrie différentielle, physique mathématique, mathématiques et société (II) - Volume en l'honneur de Jean-Pierre Bourguignon
AU  - Collectif
ED  - Hijazi Oussama
T3  - Astérisque
PY  - 2008
SP  - 23
EP  - 38
IS  - 322
PB  - Société mathématique de France
UR  - https://www.numdam.org/item/AST_2008__322__23_0/
LA  - en
ID  - AST_2008__322__23_0
ER  - 
%0 Book Section
%A Chang, Sun-Yung Alice
%A Yang, Paul C.
%T The $Q$-curvature equation in conformal geometry
%B Géométrie différentielle, physique mathématique, mathématiques et société (II) - Volume en l'honneur de Jean-Pierre Bourguignon
%A Collectif
%E Hijazi Oussama
%S Astérisque
%D 2008
%P 23-38
%N 322
%I Société mathématique de France
%U https://www.numdam.org/item/AST_2008__322__23_0/
%G en
%F AST_2008__322__23_0
Chang, Sun-Yung Alice; Yang, Paul C. The $Q$-curvature equation in conformal geometry, dans Géométrie différentielle, physique mathématique, mathématiques et société (II) - Volume en l'honneur de Jean-Pierre Bourguignon, Astérisque, no. 322 (2008), pp. 23-38. https://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 | EuDML | Zbl

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

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

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

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

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

[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 | Zbl

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

[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. | MR | Zbl | DOI

[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. | MR | Zbl | DOI

[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. | MR | Zbl | DOI

[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 | Zbl

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

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

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

[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 | Zbl | EuDML

[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. | MR | Zbl | DOI

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

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

[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. | MR | Zbl | DOI

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

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

[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. | MR | Zbl | DOI

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