Prescribing scalar curvature on $S^3$

Schneider, Matthias

Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 4, pp. 563-587.

[1] Ambrosetti A., Badiale M., Homoclinics: Poincaré-Melnikov type results via a variational approach, Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (2) (1998) 233-252. | Numdam | Zbl

[2] Ambrosetti A., Garcia Azorero J., Peral I., Perturbation of $\Delta u+u^{(N+2)/(N-2)}=0$, the scalar curvature problem in $R^N$, and related topics, J. Funct. Anal. 165 (1) (1999) 117-149. | MR | Zbl

[3] Aubin T., Some Nonlinear Problems in Riemannian Geometry, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 1998. | MR | Zbl

[4] Aubin T., Bahri A., Une hypothèse topologique pour le problème de la courbure scalaire prescrite, J. Math. Pures Appl. (9) 76 (10) (1997) 843-850. | MR | Zbl

[5] Bahri A., Coron J.-M., The scalar-curvature problem on the standard three-dimensional sphere, J. Funct. Anal. 95 (1) (1991) 106-172. | MR | Zbl

[6] Bianchi G., Non-existence and symmetry of solutions to the scalar curvature equation, Comm. Partial Differential Equations 21 (1-2) (1996) 229-234. | Zbl

[7] Bourguignon J.-P., Ezin J.-P., Scalar curvature functions in a conformal class of metrics and conformal transformations, Trans. Amer. Math. Soc. 301 (2) (1987) 723-736. | MR | Zbl

[8] Brezis H., Kato T., Remarks on the Schrödinger operator with singular complex potentials, J. Math. Pures Appl. (9) 58 (2) (1979) 137-151. | MR | Zbl

[9] Caffarelli L.A., Gidas B., Spruck J., Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math. 42 (3) (1989) 271-297. | MR | Zbl

[10] Chang S.-Y.A., Gursky M.J., Yang P.C., The scalar curvature equation on 2- and 3-spheres, Calc. Var. Partial Differential Equations 1 (2) (1993) 205-229. | MR | Zbl

[11] Chen C.-C., Lin C.-S., Prescribing scalar curvature on $S^N$. I. A priori estimates, J. Differential Geom. 57 (1) (2001) 67-171. | MR | Zbl

[12] Chen W., Li C., Prescribing scalar curvature on $S^n$, Pacific J. Math. 199 (1) (2001) 61-78. | MR | Zbl

[13] Gidas B., Ni W.M., Nirenberg L., Symmetry of positive solutions of nonlinear elliptic equations in $R^n$, in: Mathematical Analysis and Applications, Part A, Adv. in Math. Suppl. Stud., vol. 7, Academic Press, New York, 1981, pp. 369-402. | MR | Zbl

[14] Kazdan J.L., Warner F.W., Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvatures, Ann. of Math. (2) 101 (1975) 317-331. | MR | Zbl

[15] Li Y.Y., Prescribing scalar curvature on $S^n$ and related problems. I, J. Differential Equations 120 (2) (1995) 319-410. | MR | Zbl

[16] Li Y.Y., Prescribing scalar curvature on $S^n$ and related problems. II. Existence and compactness, Comm. Pure Appl. Math. 49 (6) (1996) 541-597. | MR | Zbl

[17] M. Schneider, A priori estimates for the prescribed scalar curvature equation on $S^3$, preprint, 2004.

[18] Schoen R., Zhang D., Prescribed scalar curvature on the n-sphere, Calc. Var. Partial Differential Equations 4 (1) (1996) 1-25. | MR | Zbl