A conformally invariant sphere theorem in four dimensions
Publications Mathématiques de l'IHÉS, Volume 98 (2003), pp. 105-143.
@article{PMIHES_2003__98__105_0,
     author = {Chang, Sun-Yung A. and Gursky, Matthew J. and Yang, Paul C.},
     title = {A conformally invariant sphere theorem in four dimensions},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {105--143},
     publisher = {Springer},
     volume = {98},
     year = {2003},
     doi = {10.1007/s10240-003-0017-z},
     mrnumber = {2031200},
     zbl = {1066.53079},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1007/s10240-003-0017-z/}
}
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Chang, Sun-Yung A.; Gursky, Matthew J.; Yang, Paul C. A conformally invariant sphere theorem in four dimensions. Publications Mathématiques de l'IHÉS, Volume 98 (2003), pp. 105-143. doi : 10.1007/s10240-003-0017-z. http://archive.numdam.org/articles/10.1007/s10240-003-0017-z/

1. D. Adams, A sharp inequlity of J. Moser for higher derivatives. Annals of Math., 128 (1988), 385-398. | MR | Zbl

2. A. Besse, Einstein Manifolds. Berlin: Springer-Verlag (1987). | MR | Zbl

3. T. Branson and B. Orsted, Explicit functional determinants in four dimensions. Proc. A.M.S., 113 (1991), 669-682. | MR | Zbl

4. S. Y. A. Chang, M. J. Gursky, and P. Yang, An equation of Monge-Ampere type in conformal geometry, and four-manifolds of positive Ricci curvature. Annals of Math., 155 (2002), 711-789. | MR | Zbl

5. S. Y. A. Chang, M. J. Gursky, and P. Yang, An a priori estimate for a fully nonlinear equation on four-manifolds. J. D'Analyse Math., 87 (2002), to appear. | Zbl

6. S. Y. A. Chang, M. J. Gursky, and P. Yang, Regularity of a fourth order nonlinear PDE with critical exponent. Amer. J. Math., 121 (1999), 215-257. | MR | Zbl

7. S. Y. A. Chang and P. Yang, Extremal metrics of zeta function determinants on 4-manifolds. Annals of Math., 142 (1995), 171-212. | MR | Zbl

8. J. Cheeger, W. Müller, and R. Schrader, On the curvature of piecewise flat spaces. Comm. Math. Phys., 92 (1984), 405-454. | MR | Zbl

9. A. Derdzinski, Self-dual Kähler manifolds and Einstein manifolds of dimension four. Compositio Math., 49 (1983), 405-433. | Numdam | MR | Zbl

10. L. C. Evans, Classical solutions of fully nonlinear, convex, second-order elliptic equations. Comm. Pure Appl. Math., 35 (1982), 333-363. | MR | Zbl

11. M. Freedman, The topology of four-dimensional manifolds. J. Diff. Geom., 17 (1982), 357-453. | MR | Zbl

12. M. Gursky, The Weyl functional, deRham cohomology, and Kähler-Einstein metrics. Annals of Math., 148 (1998), 315-337. | MR | Zbl

13. D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order. Berlin, Heidelberg: Springer (1983). | MR | Zbl

14. R. Hamilton, Four-manifolds with positive curvature operator. J. Diff. Geom., 24 (1986), 153-179. | MR | Zbl

15. N. Hitchin, On compact four-dimensional Einstein manifolds. J. Diff. Geom., 9 (1974), 435-442. | MR | Zbl

16. G. Huisken, Ricci deformation of the metric on a Riemannian manifold. J. Diff. Geom., 21 (1985), 47-62. | MR | Zbl

17. N. V. Krylov, Boundedly inhomogeneous elliptic and parabolic equations in a domain. Izv. Akad. Mauk. SSSR Ser. Mat., 47 (1983), 75-108. | MR | Zbl

18. Y. Li, Degree theory for second order nonlinear elliptic operators and its applications. Comm. PDE, 14 (1989), 1547-1578. | MR | Zbl

19. C. Margerin, Pointwise pinched manifolds are Spaceforms 44 (1986). AMS Proc. of Symp. in Pure Math., Arcata '84, 307-328. | Zbl

20. C. Margerin, A sharp characterization of the smooth 4-sphere in curvature terms. Comm. Anal. Geom., 6 (1998), 21-65. | MR | Zbl

21. P. Petersen, Riemannian Geometry. Springer Graduate Texts in Mathematics 171. New York (1998). | MR | Zbl

22. I. Singer and J. Thorpe, The curvature of four-dimensional Einstein spaces, in Global Analysis (Papers in honor of K. Kodaira), D. Spencer and S. Iyanaga (eds.), pp. 355-365. Tokyo: University of Tokyo Press (1969). | MR | Zbl

23. K. Uhlenbeck and J. Viaclovsky, Regularity of weak solutions to critical exponent variational equations. Math. Res. Lett., 7 (2000), 651-656. | MR | Zbl

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