Skip to main content
SpringerLink
Log in

Regularity properties of the degenerate Monge-Ampère equations on compact Kähler manifolds

  • Published:
Chinese Annals of Mathematics, Series B Aims and scope Submit manuscript

Abstract

The author establishes a result concerning the regularity properties of the degenerate complex Monge-Ampére equations on compact Kähler manifolds.

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

Similar content being viewed by others

References

  1. Aubin, T., Some Nonlinear Problems in Riemannian Geometry, Springer-Verlag, New York, 1998.

    MATH  Google Scholar 

  2. Cascini, P. and La Nave, G., Kähler-Ricci Flow and the Minimal Model Program for Projective Varieties, preprint. arXiv: math.AG/0603064

  3. Demailly, J.-P., Regularization of closed positive currents and intersection theory, J. Alg. Geom., 1, 1992, 361–409.

    MATH  MathSciNet  Google Scholar 

  4. Demailly, J.-P. and Kollár, J., Semicontinuity of complex singularity exponents and Kähler-Einstein metrics on Fano orbifolds, Ann. Ec. Norm. Sup., 34, 2001, 525–556. arXiv: math.AG/9910118

    MATH  Google Scholar 

  5. Demailly, J.-P. and Păun M., Numerical characterization of the Kähler cone of a compact Kähler manifold, Ann. Math. (2), 159(3), 2004, 1247–1274.

    Article  MATH  Google Scholar 

  6. Demailly, J.-P. and Pali, N., Degenerate complex Monge-Ampère equations over compact Kähler manifolds, preprint. arXiv: 07105109V2

  7. Eyssidieux, Ph., Guedj, V. and Zeriahi, A., Singular Kähler-Einstein metrics, J. Amer. Math. Soc., to appear. arXiv: math.AG/0603431

  8. Kolodziej, S., The complex Monge-Ampère equation, Acta Math., 180, 1998, 69–117.

    Article  MATH  MathSciNet  Google Scholar 

  9. Kolodziej, S. and Tian, G., A uniform L ∞ estimate for complex Monge-Ampère equations, Math. Ann., 342(4), 2008, 773–787. arXiv: 0710.1144

    Article  MATH  MathSciNet  Google Scholar 

  10. Siu, Y.-T., Analyticity of sets associated to Lelong numbers and the extension of closed positive currents, Invent. Math., 27, 1974, 53–156.

    Article  MATH  MathSciNet  Google Scholar 

  11. Siu, Y.-T., Lectures on Hermitian-Einstein Metrics for Stable Bundles and Kähler-Einstein metrics, Birkhäuser Verlag, Basel, 1987.

    MATH  Google Scholar 

  12. Skoda, H., Sous-ensembles analytiques d’ordre fini ou infini dans ℂn, Bull. Soc. Math. France, 100, 1972, 353–408.

    MATH  MathSciNet  Google Scholar 

  13. Tian, G. and Zhang, Z., On the Kähler-Ricci flow of projective manifolds of general type, Chin. Ann. Math., 27B(2), 2006, 179–192.

    MathSciNet  Google Scholar 

  14. Tsuji, H., Existence and degeneration of Kähler-Einstein metrics on minimal algebraic manifolds of general type, Math. Ann., 281(1), 1988, 123–133.

    Article  MATH  MathSciNet  Google Scholar 

  15. Yau, S.-T., On the Ricci curvature of a complex Kähler manifold and the complex Monge-Ampère equation, Comm. Pure Appl. Math., 31, 1978, 339–411.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut Élie Cartan, Université Henri Poincaré, Nancy 1, BP 239, 54506, Vandoeuvre-lès-Nancy Cedex, France

    Mihai Păun

Authors
  1. Mihai Păun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mihai Păun.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Păun, M. Regularity properties of the degenerate Monge-Ampère equations on compact Kähler manifolds. Chin. Ann. Math. Ser. B 29, 623–630 (2008). https://doi.org/10.1007/s11401-007-0457-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11401-007-0457-8

Keywords

2000 MR Subject Classification

Search

Navigation