A note on the Kazdan-Warner type condition
Annales de l'I.H.P. Analyse non linéaire, Volume 13 (1996) no. 3, p. 283-292
@article{AIHPC_1996__13_3_283_0,
     author = {Han, Zheng-Chao and Li, Yan Yan},
     title = {A note on the Kazdan-Warner type condition},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {13},
     number = {3},
     year = {1996},
     pages = {283-292},
     zbl = {0863.53027},
     mrnumber = {1395673},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1996__13_3_283_0}
}
Han, Zheng-Chao; Li, Yan Yan. A note on the Kazdan-Warner type condition. Annales de l'I.H.P. Analyse non linéaire, Volume 13 (1996) no. 3, pp. 283-292. http://www.numdam.org/item/AIHPC_1996__13_3_283_0/

[A] T. Aubin, Nonlinear analysis on manifolds. Monge-Ampère equations, Springer-Verlag, New York, 1982. | MR 681859 | Zbl 0512.53044

[BC] A. Bahri and J.M. Coron, The scalar-curvature problem on standard three-dimensional sphere, J. of Func. Anal., Vol. 95, 1991, pp. 106-172. | MR 1087949 | Zbl 0722.53032

[BiE] G. Bianchi and H. Egnell, An ODE approach to the equation Δu + Kun+2/n-2 = 0, in Rn, Math. Z., Vol. 210, 1992, pp. 137-166. | MR 1161175 | Zbl 0759.35019

[BE] J.P. Bourguignon and J.P. Ezin, Scalar curvature functions in a conformal class of metric and conformal transformations, Tran. Amer. Math. Soc., Vol. 301, 1987, pp. 723-736. | MR 882712 | Zbl 0622.53023

[CL] K.C. Chang and J.Q. Liu, On Nirenberg's problem, International J. of Math., Vol. 4, 1993, pp. 35-58. | MR 1209959 | Zbl 0786.58010

[CGY] S.Y. Chang, M.J. Gursky and P. Yang, The scalar curvature equation on 2- and 3-sphere, Calculus of Variations and Partial Differential Equations, Vol. 1, 1993, pp. 205-229. | MR 1261723 | Zbl 0822.35043

[CY1] S.Y. Chang and P. Yang, Conformal deformations of metrics on S2, J. Diff. Geom., Vol. 27, 1988, pp. 256-296. | MR 925123 | Zbl 0649.53022

[CD] W. Chen and W. Ding, Scalar curvature on Sn, Trans. Amer. Math. Soc., Vol. 303, 1987, pp. 365-382. | MR 896027 | Zbl 0635.35026

[ChL] W. Chen and C. Li, A necessary and sufficient condition for the Nirenberg problem, Comm. Pure Appl. Math., Vol. 48, 1995, pp. 657-667. | MR 1338474 | Zbl 0830.35034

[CS] K. Cheng and J. Smoller, Conformal metrics with prescribed Gaussian curvature on S2, Trans. Amer. Math. Soc., Vol. 336, 1993, pp. 219-255. | MR 1087053 | Zbl 0783.53010

[ES] J. Escobar and R. Schoen, Conformal metrics with prescribed scalar curvature, Invent. Math., Vol. 86, 1986, pp. 243-254. | MR 856845 | Zbl 0628.53041

[H] Z.C. Han, Prescribing Gaussian curvature on S2, Duke Math. J., Vol. 61, No. 3, 1990, pp. 679-703. | MR 1084455 | Zbl 0715.53034

[KW] J. Kazdan and F. Warner, Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvature, Ann. of Math., Vol. 101, 1975, pp. 317-331. | MR 375153 | Zbl 0297.53020

[K] D. Koutroufiotis, Gaussian curvature and conformal mapping, J. Diff. Geom., Vol. 7, 1972, pp. 479-488. | MR 328835 | Zbl 0268.53028

[GT] D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations, 2nd edition, Grundlehoen der mathematischen Wissenschaften 224, Springer-Verlag, 1983. | MR 737190 | Zbl 0562.35001

[HV] E. Hebey and M. Vaugon, Meilleures constantes dans le théorème d'inclusion de Sobolev et multiplicité pour les problèmes de Nirenberg et Yamabe, Indiana Univ. Math. J., Vol. 41, 1992, pp. 377-407. | MR 1183349 | Zbl 0764.53029

[H] C. Hong, A best constant and the Gaussian curvature, Proc. of Amer. Math. Soc., Vol. 97, 1986, pp. 734-747. | MR 845999 | Zbl 0603.58056

[L1] Y.Y. Li, Prescribing scalar curvature on S3 , S4 and related problems, J. Functional Analysis, Vol. 118, 1993, pp. 43-118. | MR 1245597 | Zbl 0790.53040

[L2] Y.Y. Li, Prescribing scalar curvature on Sn and related problems, Part I, J. Differential Equations, Vol. 120, 1995, pp. 319-410. | MR 1347349 | Zbl 0827.53039

[L3] Y.Y. Li, Prescribing scalar curvature on Sn and related problems, Part II: Existence and compactness, Comm. Pure Appl. Math., Vol. 49, 1996. | MR 1383201 | Zbl 0849.53031

[M] J. Moser, On a nonlinear problem in differential geometry, Dynamical systems (M. Peixoto, ed.) Academic Press, New York, 1973. | MR 339258

[Sc1] R. Schoen, Variational theory for the total scalar curvature functional for Riemannian metrics and related topics, in Topics in Calculus of Variations, Lecture notes in mathematics, No. 1365, edited by M. Giaquinta, Springer-Verlag, 1989, pp. 120-154. | MR 994021 | Zbl 0702.49038

[Sc2] R. Schoen, Private notes of special topics in geometry courses in Stanford University and New York University, 1988 and 1989.

[XY] X. Xu and P. Yang, Remarks on prescribing Gauss curvature, Trans. Amer. Math. Soc., Vol. 336, 1993, pp. 831-840. | MR 1087058 | Zbl 0823.53034

[Z] D. Zhang, New results on geometric variational problems, thesis, Stanford University, 1990.