Skip to main content
SpringerLink
Log in

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

  • Published:
Journal d'Analyse Mathématique Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. A. Besse,Einstein Manifolds, Springer-Verlag, Berlin, 1987.

    Book  Google Scholar 

  2. 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.

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  4. L. Fontana,Sharp boderline Sobolev inequality on compact Riemannian manifold, Comment. Math. Helv.68 (1993), 415–454.

    Article  MathSciNet  Google Scholar 

  5. 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.

    Article  MathSciNet  Google Scholar 

  6. 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.

    Article  MathSciNet  Google Scholar 

  7. N. V. Krylov,Boundedly inhomogeneous elliptic and parabolic equations in a domain, Izv. Akad. Nauk SSSR, Ser. Mat.47 (1983), 75–108.

    MathSciNet  Google Scholar 

  8. Y. Li.Degree theory for second order nonlinear elliptic operators and its applications, Comm. Partial Differential Equations14 (1989), 1541–1578.

    Article  MathSciNet  Google Scholar 

  9. J. Moser,A sharp form of an inequality by N. Trudinger, Indiana Math. J.20 (1971), 1077–1091.

    Article  MathSciNet  Google Scholar 

  10. M. Obata,The conjectures on conformal transformations of Riemannian manifolds, J. Differential Geom.6 (1971), 247–258.

    Article  MathSciNet  Google Scholar 

  11. J. Viaclovsky,Conformal geometry, contact geometry, and the calculus of variations, Duke Math. J.101 (2000), 283–316.

    Article  MathSciNet  Google Scholar 

  12. J. Viaclovsky,Estimates and existence results for some fully nonlinear elliptic equations on Riemannian manifolds, Comm. Anal. Geom., to appear.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Princeton University, 08544-1000, Princeton, NJ, USA

    Sun-Yung A. Chang

  2. Department of Mathematics, University of Notre Dame, 46556-4618, Notre Dame, IN, USA

    Matthew J. Gursky

  3. Department of Mathematics, Princeton University, 08544-1000, Princeton, NJ, USA

    Paul Yang

Authors
  1. Sun-Yung A. Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Matthew J. Gursky
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Paul Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sun-Yung A. Chang.

Additional information

Supported by NSF Grant DMS-0070542 and a Guggenheim Foundation Fellowship.

Supported in part by NSF Grant DMS-9801046 and an Alfred P. Sloan Foundation Research Fellowship.

Supported by NSF Grant DMS-0070526 and the Ellentuck Fund.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chang, SY.A., Gursky, M.J. & Yang, P. An a priori estimate for a fully nonlinear equation on four-manifolds. J. Anal. Math. 87, 151–186 (2002). https://doi.org/10.1007/BF02868472

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02868472

Search

Navigation