Opérateurs géométriques et géométrie conforme

Djadli, Zindine

Séminaire de théorie spectrale et géométrie, Tome 23 (2004-2005), pp. 49-103.

Classification : 35B33, 35J35, 53A30, 53C21

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[BCY92b] Thomas P. Branson, Sun-Yung A. Chang, and Paul C. Yang. Estimates and extremals for zeta function determinants on four-manifolds. Comm. Math. Phys., 149(2) :241–262, 1992. | MR | Zbl

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[CC86] Lennart Carleson and Sun-Yung A. Chang. On the existence of an extremal function for an inequality of J. Moser. Bull. Sci. Math. (2), 110(2) :113–127, 1986. | MR | Zbl

[CC01] Sun-Yung Alice Chang and Wenxiong Chen. A note on a class of higher order conformally covariant equations. Discrete Contin. Dynam. Systems, 7(2) :275–281, 2001. | MR | Zbl

[CGW94] S.-Y. A. Chang, M. Gursky, and T. Wolff. Lack of compactness in conformal metrics with $L^{d/2}$ curvature. J. Geom. Anal., 4(2) :143–153, 1994. | MR | Zbl

[CGY93] Sun-Yung A. Chang, Matthew J. Gursky, and Paul C. Yang. The scalar curvature equation on $2$- and $3$-spheres. Calc. Var. Partial Differential Equations, 1(2) :205–229, 1993. | MR | Zbl

[CGY99] Sun-Yung A. Chang, Matthew J. Gursky, and Paul C. Yang. Regularity of a fourth order nonlinear PDE with critical exponent. Amer. J. Math., 121(2) :215–257, 1999. | MR | Zbl

[CGY02] Sun-Yung A. Chang, Matthew J. Gursky, and Paul C. Yang. An equation of Monge-Ampère type in conformal geometry, and four-manifolds of positive Ricci curvature. Ann. of Math. (2), 155(3) :709–787, 2002. | MR | Zbl

[CGY03] Sun-Yung A. Chang, Matthew J. Gursky, and Paul C. Yang. A conformally invariant sphere theorem in four dimensions. Publ. Math. Inst. Hautes Études Sci., (98) :105–143, 2003. | EuDML | Numdam | MR | Zbl

[CGYre] Sun-Yung A. Chang, Matthew J. Gursky, and Paul C. Yang. A conformally invariant sphere theorem in four dimensions. Publ. Math. Inst. Hautes Études Sci., A paraître. | EuDML | Numdam | MR | Zbl

[Cha87] Sun-Yung A. Chang. Extremal functions in a sharp form of Sobolev inequality. In Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), pages 715–723, Providence, RI, 1987. Amer. Math. Soc. | MR | Zbl

[Cha96] Sun-Yung Alice Chang. The Moser-Trudinger inequality and applications to some problems in conformal geometry. In Nonlinear partial differential equations in differential geometry (Park City, UT, 1992), volume 2 of IAS/Park City Math. Ser., pages 65–125. Amer. Math. Soc., Providence, RI, 1996. | MR | Zbl

[Cha97] Sun-Yung Alice Chang. On zeta functional determinant. In Partial differential equations and their applications (Toronto, ON, 1995), volume 12 of CRM Proc. Lecture Notes, pages 25–50. Amer. Math. Soc., Providence, RI, 1997. With notes taken by Jie Qing. | MR | Zbl

[Cha99] Sun-Yung A. Chang. On a fourth-order partial differential equation in conformal geometry. In Harmonic analysis and partial differential equations (Chicago, IL, 1996), Chicago Lectures in Math., pages 127–150. Univ. Chicago Press, Chicago, IL, 1999. | MR | Zbl

[CL03] Chiun-Chuan Chen and Chang-Shou Lin. Topological degree for a mean field equation on Riemann surfaces. Comm. Pure Appl. Math., 56(12) :1667–1727, 2003. | MR | Zbl

[CQ96] Sun-Yung A. Chang and Jie Qing. Zeta functional determinants on manifolds with boundary. Math. Res. Lett., 3(1) :1–17, 1996. | MR | Zbl

[CQ97a] Sun-Yung A. Chang and Jie Qing. The zeta functional determinants on manifolds with boundary. I. The formula. J. Funct. Anal., 147(2) :327–362, 1997. | MR | Zbl

[CQ97b] Sun-Yung A. Chang and Jie Qing. The zeta functional determinants on manifolds with boundary. II. Extremal metrics and compactness of isospectral set. J. Funct. Anal., 147(2) :363–399, 1997. | MR | Zbl

[CQY] Sun-Yung A. Chang, Jie Qing, and Paul C. Yang. On the topology of conformally compact einstein 4-manifolds. J. Reine Angew. Math., A paraître.

[CQY00] Sun-Yung A. Chang, Jie Qing, and Paul C. Yang. Compactification of a class of conformally flat 4-manifold. Invent. Math., 142(1) :65–93, 2000. | MR | Zbl

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[CXY98] Sun-Yung A. Chang, Xingwang Xu, and Paul C. Yang. A perturbation result for prescribing mean curvature. Math. Ann., 310(3) :473–496, 1998. | MR | Zbl

[CY87] Sun-Yung Alice Chang and Paul C. Yang. Prescribing Gaussian curvature on $S^2$. Acta Math., 159(3-4) :215–259, 1987. | MR | Zbl

[CY88] Sun-Yung A. Chang and Paul C. Yang. Conformal deformation of metrics on $S^2$. J. Differential Geom., 27(2) :259–296, 1988. | MR | Zbl

[CY89a] Sun-Yung A. Chang and Paul C. Yang. Compactness of isospectral conformal metrics on $S^3$. Comment. Math. Helv., 64(3) :363–374, 1989. | EuDML | MR | Zbl

[CY89b] Sun-Yung A. Chang and Paul C. Yang. The conformal deformation equation and isospectral set of conformal metrics. In Recent developments in geometry (Los Angeles, CA, 1987), volume 101 of Contemp. Math., pages 165–178. Amer. Math. Soc., Providence, RI, 1989. | MR | Zbl

[CY90] Sun-Yung A. Chang and Paul C.-P. Yang. Isospectral conformal metrics on $3$-manifolds. J. Amer. Math. Soc., 3(1) :117–145, 1990. | MR | Zbl

[CY91a] Sun-Yung A. Chang and Paul C. Yang. A perturbation result in prescribing scalar curvature on $S^n$. Duke Math. J., 64(1) :27–69, 1991. | MR | Zbl

[CY91b] Sun-Yung A. Chang and Paul C. Yang. Spectral invariants of conformal metrics. In Harmonic analysis (Sendai, 1990), ICM-90 Satell. Conf. Proc., pages 51–60. Springer, Tokyo, 1991. | MR | Zbl

[CY93] Sun-Yung Alice Chang and Paul C. Yang. Addendum to : “A perturbation result in prescribing scalar curvature on $S^n$” [Duke Math. J. 64 (1991), no. 1, 27–69 ; MR 92m :53063]. Duke Math. J., 71(1) :333–335, 1993. | Zbl

[CY95a] Luis A. Caffarelli and Yi Song Yang. Vortex condensation in the Chern-Simons Higgs model : an existence theorem. Comm. Math. Phys., 168(2) :321–336, 1995. | MR | Zbl

[CY95b] Sun-Yung A. Chang and Paul C. Yang. Extremal metrics of zeta function determinants on $4$-manifolds. Ann. of Math. (2), 142(1) :171–212, 1995. | MR | Zbl

[CY97a] Sun-Yung A. Chang and Paul C. Yang. Determinants and extremal metrics in conformal geometry. In Geometry from the Pacific Rim (Singapore, 1994), pages 37–57. de Gruyter, Berlin, 1997. | MR | Zbl

[CY97b] Sun-Yung A. Chang and Paul C. Yang. On uniqueness of solutions of $n$th order differential equations in conformal geometry. Math. Res. Lett., 4(1) :91–102, 1997. | MR | Zbl

[CY99] Sun-Yung A. Chang and Paul C. Yang. On a fourth order curvature invariant. In Spectral problems in geometry and arithmetic (Iowa City, IA, 1997), volume 237 of Contemp. Math., pages 9–28. Amer. Math. Soc., Providence, RI, 1999. | MR | Zbl

[CY00] Sun-Yung A. Chang and Paul C. Yang. Fourth order equations in conformal geometry. In Global analysis and harmonic analysis (Marseille-Luminy, 1999), volume 4 of Sémin. Congr., pages 155–165. Soc. Math. France, Paris, 2000. | MR | Zbl

[DD01] Zindine Djadli and Olivier Druet. Extremal functions for optimal Sobolev inequalities on compact manifolds. Calc. Var. Partial Differential Equations, 12(1) :59–84, 2001. | MR | Zbl

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[DHL00] Zindine Djadli, Emmanuel Hebey, and Michel Ledoux. Paneitz-type operators and applications. Duke Math. J., 104(1) :129–169, 2000. | MR | Zbl

[DJ02] Zindine Djadli and Antoinette Jourdain. Nodal solutions for scalar curvature type equations with perturbation terms on compact Riemannian manifolds. Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8), 5(1) :205–226, 2002. | EuDML | MR | Zbl

[Dja] Zindine Djadli. Existence result for the mean field problem on Riemann surfaces of all genuses. Préprint.

[Dja99a] Zindine Djadli. Nonlinear elliptic equations involving critical Sobolev exponent on compact Riemannian manifolds in presence of symmetries. Rev. Mat. Complut., 12(1) :201–229, 1999. | EuDML | MR | Zbl

[Dja99b] Zindine Djadli. Nonlinear elliptic equations with critical Sobolev exponent on compact Riemannian manifolds. Calc. Var. Partial Differential Equations, 8(4) :293–326, 1999. | MR | Zbl

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[DMa] Zindine Djadli and Andrea Malchiodi. Existence of conformal metrics with constant $Q$-curvature. préprint, ArXiv : math.AP/0410141, À paraître dans Annals of Mathematics.

[DMb] Zindine Djadli and Andrea Malchiodi. A fourth order uniformization theorem on some four manifolds with large total $Q$-curvature. C. R. Acad. Sci. Paris, Ser. I 340 (2005), 341-346. | MR | Zbl

[DMA02] Zindine Djadli, Andrea Malchiodi, and Mohameden Ould Ahmedou. Prescribing a fourth order conformal invariant on the standard sphere. I. A perturbation result. Commun. Contemp. Math., 4(3) :375–408, 2002. | MR | Zbl

[DMOA] Zindine Djadli, Andrea Malchiodi, and Mohameden Ould Ahmedou. The prescribed boundary men curvature problem on ${\mathrm{B}}^4$. préprint. | MR | Zbl

[DMOA02] Zindine Djadli, Andrea Malchiodi, and Mohameden Ould Ahmedou. Prescribing a fourth order conformal invariant on the standard sphere, part ii : Blow-up analysis and applications. Annali della Scuola Normale Superiore di Pisa, 1(2) :387–434, 2002. | EuDML | Numdam | MR | Zbl

[DMOA03] Zindine Djadli, Andrea Malchiodi, and Mohameden Ould Ahmedou. Prescribing scalar and boundary mean curvature on the three dimensional half sphere. J. Geom. Anal., 13(2) :233–267, 2003. | MR | Zbl

[EG] José Escobar and G. Garcia. Conformal metrics on the ball with zero scalar curvature and prescribed mean curvature on the boundary. préprint. | MR | Zbl

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