@article{SIGMA_2007_3_a119,
author = {Andrea Malchiodi},
title = {Conformal {Metrics} with {Constant} $Q${-Curvature}},
journal = {Symmetry, integrability and geometry: methods and applications},
year = {2007},
volume = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a119/}
}
Andrea Malchiodi. Conformal Metrics with Constant $Q$-Curvature. Symmetry, integrability and geometry: methods and applications, Tome 3 (2007). http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a119/
[1] Adams D., “A sharp inequality of J. Moser for higher order derivatives”, Ann. of Math. (2), 128 (1988), 385–398 | DOI | MR | Zbl
[2] Bahri A., Critical points at infinity in some variational problems, Research Notes in Mathematics, 182, Longman-Pitman, London, 1989 | MR | Zbl
[3] Bahri A., Coron J. M., “On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of the topology of the domain”, Comm. Pure Appl. Math., 41 (1988), 253–294 | DOI | MR | Zbl
[4] Branson T. P., The functional determinant, Global Analysis Research Center Lecture Note Series, 4, Seoul National University, 1993 | MR | Zbl
[5] Branson T. P., “Differential operators canonically associated to a conformal structure”, Math. Scand., 57 (1985), 293–345 | MR | Zbl
[6] Branson T. P., Gover A. R., “Conformally invariant operators, differential forms, cohomology and a generalisation of $Q$-curvature”, Comm. Partial Differential Equations, 30 (2005), 1611–1669 ; math.DG/0309085 | DOI | MR | Zbl
[7] Branson T. P., Ørsted B., “Explicit functional determinants in four dimensions”, Proc. Amer. Math. Soc., 113 (1991), 669–682 | DOI | MR | Zbl
[8] Branson T. P., Chang S. Y. A., Yang P. C., “Estimates and extremal problems for the log-determinant on $4$-manifolds”, Comm. Math. Phys., 149 (1992), 241–262 | DOI | MR | Zbl
[9] Bredon G. E., Topology and geometry, Graduate Texts in Mathematics, 139, Springer, 1997 | MR | Zbl
[10] Brendle S., “Global existence and convergence for a higher order flow in conformal geometry”, Ann. of Math. (2), 158 (2003), 323–343 ; math.DG/0404415 | DOI | MR | Zbl
[11] Brendle S., “Prescribing a higher order conformal invariant on $S^n$”, Comm. Anal. Geom., 11 (2003), 837–858 | MR | Zbl
[12] Chang S. Y. A., Gursky M. J., Yang P. C., “An equation of Monge–Ampère type in conformal geometry, and four-manifolds of positive Ricci curvature”, Ann. of Math. (2), 155 (2002), 709–787 ; math.DG/0409583 | DOI | MR | Zbl
[13] Chang S. Y. A., Gursky M. J., Yang P. C., “A conformally invariant sphere theorem in four dimensions”, Publ. Math. Inst. Hautes Études Sci., 98 (2003), 105–143 ; math.DG/0309287 | MR | Zbl
[14] Chang S. Y. A., Qing J., “The zeta functional determinants on manifolds with boundary. I. The formula”, J. Funct. Anal., 147 (1997), 327–362 | DOI | MR | Zbl
[15] Chang S. Y. A., Qing J., “The zeta functional determinants on manifolds with boundary. II. Extremal metrics and compactness of isospectral set”, J. Funct. Anal., 147 (1997), 363–399 | DOI | MR | Zbl
[16] Chang S. Y. A., Qing J., Yang P. C., “Compactification of a class of conformally flat 4-manifold”, Invent. Math., 142 (2000), 65–93 | DOI | MR | Zbl
[17] Chang S. Y. A., Qing J., Yang P. C., “On the Chern–Gauss–Bonnet integral for conformal metrics on $R^4$”, Duke Math. J., 103 (2000), 523–544 | DOI | MR | Zbl
[18] Chang S. Y. A., Yang P. C., “Extremal metrics of zeta functional determinants on $4$-manifolds”, Ann. of Math. (2), 142 (1995), 171–212 | DOI | MR | Zbl
[19] Chang S. Y. A., Yang P. C., “On a fourth order curvature invariant”, Spectral Problems in Geometry and Arithmetic, Comtemp. Math., 237, ed. T. Branson, 1999, 9–28 | MR | Zbl
[20] Chen C. C., Lin C. S., “Topological degree for a mean field equation on Riemann surfaces”, Comm. Pure Appl. Math., 56 (2003), 1667–1727 | DOI | MR | Zbl
[21] Chen W., Li C., “Prescribing Gaussian curvatures on surfaces with conical singularities”, J. Geom. Anal., 1 (1991), 359–372 | MR | Zbl
[22] Ding W., Jost J., Li J., Wang G., “Existence results for mean field equations”, Ann. Inst. H. Poincaré Anal. Non Linéaire, 16 (1999), 653–666 ; dg-ga/9710023 | DOI | MR | Zbl
[23] Djadli Z., Malchiodi A., “A fourth order uniformization theorem on some four manifolds with large total $Q$-curvature”, C. R. Math. Acad. Sci. Paris, 340 (2005), 341–346 | MR | Zbl
[24] Djadli Z., Malchiodi A., “Existence of conformal metrics with constant $Q$-curvature”, Ann. of Math. (2), 168:3 (2008), 813–858 ; math.DG/0410141 | DOI | MR | Zbl
[25] Druet O., Robert F., “Bubbling phenomena for fourth-order four-dimensional pdes with exponential growth”, Proc. Amer. Math. Soc., 134 (2006), 897–908 | DOI | MR | Zbl
[26] Fefferman C., Graham C. R., “$Q$-curvature and Poincaré metrics”, Math. Res. Lett., 9 (2002), 139–151 | MR | Zbl
[27] Fefferman C., Hirachi K., “Ambient metric construction of $Q$-curvature in conformal and CR geometries”, Math. Res. Lett., 10 (2003), 819–832 ; math.DG/0303184 | MR
[28] Gover A. R., “Invariants and calculus for conformal geometry”, Adv. Math., 163 (2001), 206–257 | DOI | MR | Zbl
[29] Gover A. R., Peterson L. J., “The ambient obstruction tensor and the conformal deformation complex”, Pacific J. Math., 226 (2006), 309–351 ; math.DG/0408229 | DOI | MR | Zbl
[30] Graham C. R., Jenne R., Mason L. J., Sparling G., “Conformally invariant powers of the Laplacian. I. Existence”, J. London Math. Soc., 46 (1992), 557–565 | DOI | MR | Zbl
[31] Graham C. R., Juhl A., Holographic formula for $Q$-curvature, arXiv:0704.1673 | MR
[32] Graham C. R., Zworski M., “Scattering matrix in conformal geometry”, Invent. Math., 152 (2003), 89–118 ; math.DG/0109089 | DOI | MR | Zbl
[33] Gursky M., “The Weyl functional, de Rham cohomology, and Kahler–Einstein metrics”, Ann. of Math. (2), 148 (1998), 315–337 | DOI | MR | Zbl
[34] Gursky M., “The principal eigenvalue of a conformally invariant differential operator, with an application to semilinear elliptic PDE”, Comm. Math. Phys., 207 (1999), 131–143 | DOI | MR | Zbl
[35] Gursky M., Viaclovsky J., “A fully nonlinear equation on four-manifolds with positive scalar curvature”, J. Differential Geom., 63 (2003), 131–154 ; math.DG/0301350 | MR | Zbl
[36] Li J., Li Y., Liu P., The $Q$-curvature on a 4-dimensional Riemannian manifold $(M,g)$ with $\int_MQ\,dV_g=8\pi^2$, math.DG/0608543
[37] Malchiodi A., “Compactness of solutions to some geometric fourth-order equations”, J. Reine Angew. Math., 594 (2006), 137–174 ; math.AP/0410140 | MR | Zbl
[38] Malchiodi A., Morse theory and a scalar field equation on compact surfaces, Preprint | MR
[39] Malchiodi A., Struwe M., “$Q$-curvature flow on $S^4$”, J. Differential Geom., 73 (2006), 1–44 | MR | Zbl
[40] Ndiaye C. B., “Constant $Q$-curvature metrics in arbitrary dimension”, J. Funct. Anal., 251:1 (2007), 1–58 | DOI | MR | Zbl
[41] Ndiaye C. B., Conformal metrics with constant $Q$-curvature for manifolds with boundary, Preprint, 2007 | MR
[42] Ndiaye C. B., Constant $T$-curvature conformal metrics on 4-manifolds with boundary, arXiv:0708.0732 | MR
[43] Paneitz S., A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds, Preprint, 1983
[44] Struwe M., “The existence of surfaces of constant mean curvature with free boundaries”, Acta Math., 160 (1988), 19–64 | DOI | MR | Zbl
[45] Struwe M., Variational methods. Applications to nonlinear partial differential equations and Hamiltonian systems, 3rd ed., Springer-Verlag, Berlin, 2000 | MR | Zbl
[46] Wei J., Xu X., “On conformal deformations of metrics on $S^n$”, J. Funct. Anal, 157 (1998), 292–325 | DOI | MR | Zbl