On a fully nonlinear Yamabe problem

Annales Scientifiques de l'Ecole Normale Superieure

Volumn 39, Issue 4, 2006, Pages 569-598

  Ge, Yuxin ^a   Wang, Guofang ^b  

^a UFR des Sciences et Technologie   (France)

^b MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846004437     PISSN: 00129593     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ansens.2005.12.007     Document Type: Article

References (42)

1. Andrews B. Monotone quantities and unique limits for evolving convex hypersurfaces. Internat. Math. Res. Notices 1997 (1997) 1001-1031
2. Aubin T. Équations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire. J. Math. Pures Appl. 55 (1976) 269-296
3. Aubin T., and Li Y. On the best Sobolev inequality. J. Math. Pures Appl. 78 (1999) 353-387
4. n / 2. Calc. Var. Partial Differential Equations 20 (2004) 399-402
5. Caffarelli L., Nirenberg L., and Spruck J. The Dirichlet problem for nonlinear second-order elliptic equations. III. Functions of the eigenvalues of the Hessian. Acta Math. 155 (1985) 261-301
6. Chang A., Gursky M., and Yang P. An equation of Monge-Ampère type in conformal geometry, and four manifolds of positive Ricci curvature. Ann. of Math. 155 (2002) 709-787
7. Chang A., Gursky M., and Yang P. An a priori estimate for a fully nonlinear equation on Four-manifolds. J. Anal. Math. 87 (2002) 151-186
8. Chang A., Gursky M., and Yang P. Entire solutions of a fully nonlinear equation. Lectures on Partial Differential Equations. New Stud. Adv. Math. vol. 2 (2003), Int. Press, Somerville, MA 43-60
9. Chou K.-S. On a real Monge-Ampère functional (K.S. Tso). Invent. Math. 101 (1990) 425-448
10. Chou K.-S., and Wang X.-J. A variational theory of the Hessian equation. Comm. Pure Appl. Math. 54 (2001) 1029-1064
11. Garding L. An inequality for hyperbolic polynomials. J. Math. Mech. 8 (1959) 957-965
12. Ge Y., Wang G., On a conformal quotient equation, in preparation
13. González M. d. M., Removability of singularities for a class of fully non-linear elliptic equations Preprint, 2004
14. Gromov M., and Lawson H.B. The classification of simply connected manifolds of positive scalar curvature. Ann. of Math. (2) 111 (1980) 423-434
15. Guan P., Lin C.-S., and Wang G. Schouten tensor and some topological properties. Comm. Anal. Geom. 13 (2005) 845-860
16. Guan P., Lin C.-S., Wang G., Local gradient estimates for conformal quotient equations, Preprint
17. Guan P., Viaclovsky J., and Wang G. Some properties of the Schouten tensor and applications to conformal geometry. Trans. Amer. Math. Soc. 355 (2003) 925-933
18. Guan P., and Wang G. Local estimates for a class of fully nonlinear equations arising from conformal geometry. Int. Math. Res. Not. 2003 (2003) 1413-1432
19. Guan P., and Wang G. A fully nonlinear conformal flow on locally conformally flat manifolds. J. reine angew. Math. 557 (2003) 219-238
20. Guan P., and Wang G. Geometric inequalities on locally conformally flat manifolds. Duke Math. J. 124 (2004) 177-212
21. Guan P., and Wang G. A fully nonlinear conformal flow on locally conformally flat manifolds. math.DG/0112256 v1 of [19]
22. k-Yamabe problem. Adv. in Math. 187 (2004) 447-487
23. Gursky M., and Viaclovsky J. A fully nonlinear equation on 4-manifolds with positive scalar curvature. J. Differential Geom. 63 (2003) 131-154
24. Gursky M., and Viaclovsky J. Prescribing symmetric functions of the eigenvalues of the Ricci tensor. Ann of Math., submitted for publication. math.DG/0409187
25. Habermann L. Riemannian Metrics of Constant Mass and Moduli Spaces of Conformal Structures. Lecture Notes in Mathematics vol. 1743 (2000), Springer, Berlin
26. Hebey E. Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities. Courant Lecture Notes in Math. vol. 5 (1999), Courant Inst. of Math. Sci./Amer. Math. Soc., New York/Providence, RI
27. Krylov N. Nonlinear Elliptic and Parabolic Equations of the Second Order (1987), D. Reidel, Dordrecht
28. Lee J., and Parker T. The Yamabe problem. Bull. Amer. Math. Soc. (N.S.) 17 (1987) 37-91
29. Li A., and Li Y. On some conformally invariant fully nonlinear equations. Comm. Pure Appl. Math. 56 (2003) 1416-1464
30. Lions P.L. Two remarks on the Monge-Ampère. Ann. Mat. Pura Appl. 142 (1985) 263-275
31. Micallef M., and Wang M. Metrics with nonnegative isotropic curvature. Duke Math. J. 72 (1993) 649-672
32. Schoen R. Conformal deformation of a Riemannian metric to constant curvature. J. Differential Geom. 20 (1984) 479-495
33. m. J. Differential Geom. 33 (1991) 127-137
34. Sheng W., Trudinger N., and Wang X. The Yamabe problem for higher order curvatures. math.DG/0505463
35. Simon L. Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems. Ann. of Math. 118 (1983) 525-571
36. Trudinger N. On imbeddings into Orlicz spaces and some applications. J. Math. Mech. 17 (1967) 473-483
37. Trudinger N., and Wang X.-J. A Poincaré type inequality for Hessian integrals. Calc. Var. Partial Differential Equations 6 4 (1998) 315-328
38. Viaclovsky J. Conformal geometry, contact geometry and the calculus of variations. Duke J. Math. 101 2 (2000) 283-316
39. Viaclovsky J. Conformally invariant Monge-Ampère equations: Global solutions. Trans. Amer. Math. Soc. 352 (2000) 4371-4379
40. Viaclovsky J. Estimates and some existence results for some fully nonlinear elliptic equations on Riemannian manifolds. Comm. Anal. Geom. 10 (2002) 815-847
41. Wang X.J. A class of fully nonlinear elliptic equations and related functionals. Indiana Univ. Math. J. 43 (1994) 25-54
42. Yamabe H. On a deformation of Riemannian structures on compact manifolds. Osaka Math. J. 12 (1960) 21-37