A conformally invariant sphere theorem in four dimensions
Chang, Sun-Yung A. ; Gursky, Matthew J. ; Yang, Paul C.
Publications Mathématiques de l'IHÉS, Tome 98 (2003), p. 105-143 / Harvested from Numdam
@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},
     volume = {98},
     year = {2003},
     pages = {105-143},
     doi = {10.1007/s10240-003-0017-z},
     mrnumber = {2031200},
     zbl = {1066.53079},
     language = {en},
     url = {http://dml.mathdoc.fr/item/PMIHES_2003__98__105_0}
}
Chang, Sun-Yung A.; Gursky, Matthew J.; Yang, Paul C. A conformally invariant sphere theorem in four dimensions. Publications Mathématiques de l'IHÉS, Tome 98 (2003) pp. 105-143. doi : 10.1007/s10240-003-0017-z. http://gdmltest.u-ga.fr/item/PMIHES_2003__98__105_0/

1. D. Adams, A sharp inequlity of J. Moser for higher derivatives. Annals of Math., 128 (1988), 385-398. | MR 960950 | Zbl 0672.31008

2. A. Besse, Einstein Manifolds. Berlin: Springer-Verlag (1987). | MR 867684 | Zbl 0613.53001

3. T. Branson and B. Orsted, Explicit functional determinants in four dimensions. Proc. A.M.S., 113 (1991), 669-682. | MR 1050018 | Zbl 0762.47019

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 1923964 | Zbl 1031.53062

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 1067.58028

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 1680337 | Zbl 0921.35032

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 1338677 | Zbl 0842.58011

8. J. Cheeger, W. Müller, and R. Schrader, On the curvature of piecewise flat spaces. Comm. Math. Phys., 92 (1984), 405-454. | MR 734226 | Zbl 0559.53028

9. A. Derdzinski, Self-dual Kähler manifolds and Einstein manifolds of dimension four. Compositio Math., 49 (1983), 405-433. | Numdam | MR 707181 | Zbl 0527.53030

10. L. C. Evans, Classical solutions of fully nonlinear, convex, second-order elliptic equations. Comm. Pure Appl. Math., 35 (1982), 333-363. | MR 649348 | Zbl 0469.35022

11. M. Freedman, The topology of four-dimensional manifolds. J. Diff. Geom., 17 (1982), 357-453. | MR 679066 | Zbl 0528.57011

12. M. Gursky, The Weyl functional, deRham cohomology, and Kähler-Einstein metrics. Annals of Math., 148 (1998), 315-337. | MR 1652920 | Zbl 0949.53025

13. D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order. Berlin, Heidelberg: Springer (1983). | MR 737190 | Zbl 0361.35003

14. R. Hamilton, Four-manifolds with positive curvature operator. J. Diff. Geom., 24 (1986), 153-179. | MR 862046 | Zbl 0628.53042

15. N. Hitchin, On compact four-dimensional Einstein manifolds. J. Diff. Geom., 9 (1974), 435-442. | MR 350657 | Zbl 0281.53039

16. G. Huisken, Ricci deformation of the metric on a Riemannian manifold. J. Diff. Geom., 21 (1985), 47-62. | MR 806701 | Zbl 0606.53026

17. N. V. Krylov, Boundedly inhomogeneous elliptic and parabolic equations in a domain. Izv. Akad. Mauk. SSSR Ser. Mat., 47 (1983), 75-108. | MR 688919 | Zbl 0578.35024

18. Y. Li, Degree theory for second order nonlinear elliptic operators and its applications. Comm. PDE, 14 (1989), 1547-1578. | MR 1026774 | Zbl 0702.35094

19. C. Margerin, Pointwise pinched manifolds are Spaceforms 44 (1986). AMS Proc. of Symp. in Pure Math., Arcata '84, 307-328. | Zbl 0587.53042

20. C. Margerin, A sharp characterization of the smooth 4-sphere in curvature terms. Comm. Anal. Geom., 6 (1998), 21-65. | MR 1619838 | Zbl 0966.53022

21. P. Petersen, Riemannian Geometry. Springer Graduate Texts in Mathematics 171. New York (1998). | MR 1480173 | Zbl 0914.53001

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 256303 | Zbl 0199.25401

23. K. Uhlenbeck and J. Viaclovsky, Regularity of weak solutions to critical exponent variational equations. Math. Res. Lett., 7 (2000), 651-656. | MR 1809291 | Zbl 0977.58020