A conformally invariant sphere theorem in four dimensions

Sun-Yung A. Chang; Matthew J. Gursky; Paul C. Yang

Publications Mathématiques de l'IHÉS (2003)

  • Volume: 98, page 105-143
  • ISSN: 0073-8301

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Chang, Sun-Yung A., Gursky, Matthew J., and Yang, Paul C.. "A conformally invariant sphere theorem in four dimensions." Publications Mathématiques de l'IHÉS 98 (2003): 105-143. <http://eudml.org/doc/104193>.

@article{Chang2003,
author = {Chang, Sun-Yung A., Gursky, Matthew J., Yang, Paul C.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {sphere theorems; piching; conformal geometry},
language = {eng},
pages = {105-143},
publisher = {Springer},
title = {A conformally invariant sphere theorem in four dimensions},
url = {http://eudml.org/doc/104193},
volume = {98},
year = {2003},
}

TY - JOUR
AU - Chang, Sun-Yung A.
AU - Gursky, Matthew J.
AU - Yang, Paul C.
TI - A conformally invariant sphere theorem in four dimensions
JO - Publications Mathématiques de l'IHÉS
PY - 2003
PB - Springer
VL - 98
SP - 105
EP - 143
LA - eng
KW - sphere theorems; piching; conformal geometry
UR - http://eudml.org/doc/104193
ER -

References

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  1. 1. D. Adams, A sharp inequlity of J. Moser for higher derivatives. Annals of Math., 128 (1988), 385–398. Zbl0672.31008MR960950
  2. 2. A. Besse, Einstein Manifolds. Berlin: Springer-Verlag (1987). Zbl0613.53001MR867684
  3. 3. T. Branson and B. Orsted, Explicit functional determinants in four dimensions. Proc. A.M.S., 113 (1991), 669–682. Zbl0762.47019MR1050018
  4. 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. Zbl1031.53062MR1923964
  5. 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. Zbl1067.58028
  6. 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. Zbl0921.35032MR1680337
  7. 7. S. Y. A. Chang and P. Yang, Extremal metrics of zeta function determinants on 4-manifolds. Annals of Math., 142 (1995), 171–212. Zbl0842.58011MR1338677
  8. 8. J. Cheeger, W. Müller, and R. Schrader, On the curvature of piecewise flat spaces. Comm. Math. Phys., 92 (1984), 405–454. Zbl0559.53028MR734226
  9. 9. A. Derdzinski, Self-dual Kähler manifolds and Einstein manifolds of dimension four. Compositio Math., 49 (1983), 405–433. Zbl0527.53030MR707181
  10. 10. L. C. Evans, Classical solutions of fully nonlinear, convex, second–order elliptic equations. Comm. Pure Appl. Math., 35 (1982), 333–363. Zbl0469.35022MR649348
  11. 11. M. Freedman, The topology of four-dimensional manifolds. J. Diff. Geom., 17 (1982), 357–453. Zbl0528.57011MR679066
  12. 12. M. Gursky, The Weyl functional, deRham cohomology, and Kähler-Einstein metrics. Annals of Math., 148 (1998), 315–337. Zbl0949.53025MR1652920
  13. 13. D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order. Berlin, Heidelberg: Springer (1983). Zbl0361.35003MR737190
  14. 14. R. Hamilton, Four-manifolds with positive curvature operator. J. Diff. Geom., 24 (1986), 153–179. Zbl0628.53042MR862046
  15. 15. N. Hitchin, On compact four-dimensional Einstein manifolds. J. Diff. Geom., 9 (1974), 435–442. Zbl0281.53039MR350657
  16. 16. G. Huisken, Ricci deformation of the metric on a Riemannian manifold. J. Diff. Geom., 21 (1985), 47–62. Zbl0606.53026MR806701
  17. 17. N. V. Krylov, Boundedly inhomogeneous elliptic and parabolic equations in a domain. Izv. Akad. Mauk. SSSR Ser. Mat., 47 (1983), 75–108. Zbl0578.35024MR688919
  18. 18. Y. Li, Degree theory for second order nonlinear elliptic operators and its applications. Comm. PDE, 14 (1989), 1547–1578. Zbl0702.35094MR1026774
  19. 19. C. Margerin, Pointwise pinched manifolds are Spaceforms 44 (1986). AMS Proc. of Symp. in Pure Math., Arcata ’84, 307–328. Zbl0587.53042
  20. 20. C. Margerin, A sharp characterization of the smooth 4-sphere in curvature terms. Comm. Anal. Geom., 6 (1998), 21–65. Zbl0966.53022MR1619838
  21. 21. P. Petersen, Riemannian Geometry. Springer Graduate Texts in Mathematics 171. New York (1998). Zbl0914.53001MR1480173
  22. 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). Zbl0199.25401MR256303
  23. 23. K. Uhlenbeck and J. Viaclovsky, Regularity of weak solutions to critical exponent variational equations. Math. Res. Lett., 7 (2000), 651–656. Zbl0977.58020MR1809291

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