Skip to main content
Log in

Uniqueness of Kähler-Ricci solitons

  • Published:
Acta Mathematica

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

References

  1. Alexander, H. J. &Taylor, B. A., Comparison of two capacities in Cn.Math. Z., 186 (1984), 407–417.

    Article  MathSciNet  Google Scholar 

  2. Aubin, T., Réduction du cas positif de l'équation de Monge-Ampère sur les variétés kählériennes compactes à la démonstration d'une inégalité.J. Funct. Anal., 57 (1984), 143–153.

    Article  MATH  MathSciNet  Google Scholar 

  3. Bedford, E., Survey of pluri-potential theory, inSeveral Complex Variables (Stockholm, 1987/88), pp. 48–97. Math. Notes, 38. Princeton Univ. Press, Princeton, NJ, 1993.

    Google Scholar 

  4. Bando, S. &Mabuchi, T., Uniqueness of Einstein-Kähler metrics modulo connected group actions, inAlgebraic Geometry (Sendai, 1985), pp. 11–40. Adv. Stud. Pure Math., 10. North-Holland, Amsterdam-New York, 1987.

    Google Scholar 

  5. Bedford, E. &Taylor, B. A., The Dirichlet problem for a complex Monge-Ampère equation.Invent. Math., 37 (1976), 1–44.

    Article  MathSciNet  Google Scholar 

  6. —, A new capacity for plurisubharmonic functions.Acta Math., 149 (1982), 1–40.

    MathSciNet  Google Scholar 

  7. Cao, H.-D., Existence of gradient Kähler-Ricci solitons, inElliptic and Parabolic Methods in Geometry (Minneapolis, MN, 1994), pp. 1–16. AK Peters, Wellesley, MA, 1996.

    Google Scholar 

  8. —, Limits of solutions to the Kähler-Ricci flow.J. Differential Geom., 45 (1997), 257–272.

    MATH  MathSciNet  Google Scholar 

  9. Calabi, E., Extremal Kähler metrics, II, inDifferential Geometry and Complex Analysis, pp. 95–114. Springer-Verlag, Berlin-New York, 1985.

    Google Scholar 

  10. Futaki, A., An obstruction to the existence of Einstein Kähler metrics.Invent. Math., 73 (1983), 437–443.

    Article  MATH  MathSciNet  Google Scholar 

  11. —,Kähler-Einstein Metrics and Integral Invariants. Lecture Notes in Math., 1314. Springer-Verlag, Berlin-New York, 1988.

    Google Scholar 

  12. Futaki, A. &Mabuchi, T., Bilinear forms and extremal Kähler vector fields associated with Kähler classes.Math. Ann., 301 (1995), 199–210.

    Article  MathSciNet  Google Scholar 

  13. Hamilton, R. S., Eternal solutions to the Ricci flow.J. Differential Geom., 38 (1993), 1–11.

    MATH  MathSciNet  Google Scholar 

  14. Koiso, N., On rationally symmetric Hamilton's equation for Kähler-Einstein metrics, inRecent Topics in Differential and Analytic Geometry, pp. 327–337. Adv. Stud. Pure Math., 18-I. Academic Press, Boston, MA, 1990.

    Google Scholar 

  15. Kołodziej, S., The complex Monge-Ampère equation.Acta Math., 180 (1998), 69–117.

    MathSciNet  Google Scholar 

  16. Tian, G., Kähler-Einstein metrics on algebraic manifolds, inTranscendental Methods in Algebraic Geometry (Cetraro, 1994), pp. 143–185. Lecture Notes in Math., 1646. Springer-Verlag, Berlin, 1996.

    Google Scholar 

  17. — Kähler-Einstein metrics with positive scalar curvature.Invent. Math., 130 (1997), 1–37.

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  19. Zhu, X. H., Ricci soliton-typed equations on compact complex manifolds withc 1(M)>0. To appear inJ. Geom. Anal., 10 (2000).

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tian, G., Zhu, X. Uniqueness of Kähler-Ricci solitons. Acta Math. 184, 271–305 (2000). https://doi.org/10.1007/BF02392630

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02392630

Keywords

Navigation