Journal d’Analyse Mathématique

, Volume 87, Issue 1, pp 151–186

An a priori estimate for a fully nonlinear equation on four-manifolds

  • Sun-Yung A. Chang
  • Matthew J. Gursky
  • Paul Yang


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Be]
    A. Besse,Einstein Manifolds, Springer-Verlag, Berlin, 1987.MATHGoogle Scholar
  2. [CGY]
    S. Y. A. Chang, M. J. Gursky and P. Yang,An equation of Monge-Ampere type in conformal geometry, andfour-manifolds of positive Ricci curvature, Ann. of Math.155 (2002), 711–789.CrossRefMathSciNetGoogle Scholar
  3. [Ev]
    L. C. Evans,Classical solutions of fully nonlinear, convex, second-order elliptic equations, Comm. Pure Appl. Math.35 (1982), 333–363.MATHCrossRefMathSciNetGoogle Scholar
  4. [F]
    L. Fontana,Sharp boderline Sobolev inequality on compact Riemannian manifold, Comment. Math. Helv.68 (1993), 415–454.MATHCrossRefMathSciNetGoogle Scholar
  5. [G]
    M. J. Gursky,The principal eigenvalue of a conformally invariant differential operator, with an application to semilinear elliptic PDE, Comm. Math. Phys.207 (1999), 131–143.MATHCrossRefMathSciNetGoogle Scholar
  6. [KMPS]
    N. Korevaar, R. Mazzeo, F. Pacard and R. Schoen,Refined asymptotics for constand scalar curvature metrics with isolated singularities, Invent. Math.135 (1999), 233–272.MATHCrossRefMathSciNetGoogle Scholar
  7. [Kr]
    N. V. Krylov,Boundedly inhomogeneous elliptic and parabolic equations in a domain, Izv. Akad. Nauk SSSR, Ser. Mat.47 (1983), 75–108.MathSciNetGoogle Scholar
  8. [Li]
    Y. Li.Degree theory for second order nonlinear elliptic operators and its applications, Comm. Partial Differential Equations14 (1989), 1541–1578.MATHCrossRefMathSciNetGoogle Scholar
  9. [M]
    J. Moser,A sharp form of an inequality by N. Trudinger, Indiana Math. J.20 (1971), 1077–1091.CrossRefGoogle Scholar
  10. [Ob]
    M. Obata,The conjectures on conformal transformations of Riemannian manifolds, J. Differential Geom.6 (1971), 247–258.MATHMathSciNetGoogle Scholar
  11. [Vi1]
    J. Viaclovsky,Conformal geometry, contact geometry, and the calculus of variations, Duke Math. J.101 (2000), 283–316.MATHCrossRefMathSciNetGoogle Scholar
  12. [Vi2]
    J. Viaclovsky,Estimates and existence results for some fully nonlinear elliptic equations on Riemannian manifolds, Comm. Anal. Geom., to appear.Google Scholar

Copyright information

© Hebrew University of Jerusalem 2002

Authors and Affiliations

  • Sun-Yung A. Chang
    • 1
  • Matthew J. Gursky
    • 2
  • Paul Yang
    • 3
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA
  2. 2.Department of MathematicsUniversity of Notre DameNotre DameUSA
  3. 3.Department of MathematicsPrinceton UniversityPrincetonUSA

Personalised recommendations