Kähler-Einstein metrics on algebraic manifolds

  • Gang Tian
Part of the Lecture Notes in Mathematics book series (LNM, volume 1646)


Line Bundle Chern Class Rational Curf Bisectional Curvature Algebraic Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Au] Aubin, T.: Equations du type de Monge-Ampère sur les variétés Kähleriennes compactes. C. R. Acad. Sci. Paris 283 (1976), 119–121.MathSciNetMATHGoogle Scholar
  2. [Ba] Bando, S.: Einstein Kähler metrics of negative Ricci curvature on open Kähler manifolds, Kähler Metrics and Moduli Spaces, Adv. Studies in Pure Math., vol. 18, no. 2 (1990).Google Scholar
  3. [Be] Besse, A.: Einstein Manifolds. Ergebnisse der Mathematik und ihrer Grensgebiete, 3. Folge, Band 10, Springer-Verlag, Berlin, New York, 1987.CrossRefMATHGoogle Scholar
  4. [Bea] Beauville, A.: Variétés Kähleriennes dont la lère classe de Chern est nulle. J. Diff. Geom., 18 (1983), 755–782.MathSciNetMATHGoogle Scholar
  5. [BK] Bando, S. and Kobayashi, R.: Ricci-flat Kähler metrics on affine algebraic manifolds. Lecture Notes in Mathematics, 1339 (1987), Springer-Verlag.Google Scholar
  6. [BM] Bando, S. and Mabuchi, T.: Uniqueness of Einstein Kähler metrics modulo connected group actions. Algebraic Geometry, Adv. Studies in Pure Math., 10 (1987).Google Scholar
  7. [Bo] Bott, R.: A residue formula for holomorphic vector fields, J. Diff. Geom., 1 (1967), 311–330.MathSciNetMATHGoogle Scholar
  8. [BPV] Barth, W., Peters, C. and Van de Ven, A.: Compact Complex Surfaces. Ergebnisse der Mathematik und ihrer Grensgebiete, 3. Folge, Band 4, Springer-Verlag, Berlin, New York, 1984.CrossRefMATHGoogle Scholar
  9. [BGS] Bismut, J., Gillet, H. and Soulé, C.: Analytic torsion and holomorphic determinant bundles, I–III. Comm. Math. Phys., 115 (1988), 49–126, 301–351.MathSciNetCrossRefMATHGoogle Scholar
  10. [CKNS] Cafferalli, L., Kohn, J., Nirenberg, L. and Spruck, J.: The Dirichlet problem for nonlinear second order elliptic equations II. Comm. Pure and Appl. Math., vol. 38, no. 2 (1985), 209–255.MathSciNetCrossRefMATHGoogle Scholar
  11. [CY] Cheng, S.Y. and Yau, S.T.: Inequality between Chern numbers of singular Kähler surfaces and characterization of orbit space of discrete group of SU (2,1). Contemporary Math., 49 (1986), 31–43.MathSciNetCrossRefMATHGoogle Scholar
  12. [Di] Ding, W.: Remarks on the existence problem of positive Kähler-Einstein metrics. Math. Ann. 282 (1988), 463–471.MathSciNetCrossRefMATHGoogle Scholar
  13. [DT1] Ding, W. and Tian, G.: The generalized Moser-Trudinger Inequality. Proceedings of Nankai International Conference on Nonlinear Analysis, 1993.Google Scholar
  14. [DT2] Ding, W. and Tian, G.: Kähler-Einstein metrics and the generalized Futaki invariants. Invent. Math., 110 (1992), 315–335.MathSciNetCrossRefMATHGoogle Scholar
  15. [Ev] Evans, C.: Classical solutions of fully nonlinear, convex, second-order elliptic equations. Comm. Pure and Appl. Math., vol. 35 (1982), 333–363.MathSciNetCrossRefMATHGoogle Scholar
  16. [Fu1] Futaki, A.: An obstruction to the existence of Einstein-Kähler metrics, Inv. Math., 73 (1983), 437–443.MathSciNetCrossRefMATHGoogle Scholar
  17. [Fu2] Futaki, A.: Kähler-Einstein Metrics and Integral Invariants. Lecture Notes in Mathematics, 1314, Springer-Verlag.Google Scholar
  18. [Ko1] Kobayashi, R.: Kähler-Einstein metrics on open algebraic manifolds, Osaka J. Math., 21 (1984), 399–418.MathSciNetMATHGoogle Scholar
  19. [Ko2] Kobayashi, R.: Einstein-Kähler metrics on open algebraic surfaces of general type. Tohoku Math. J., 37 (1985), 43–77.MathSciNetCrossRefMATHGoogle Scholar
  20. [Kob] Kobayashi, S.: The first Chern class and holomorphic symmetric tensor fields. Math. Soc. Japan, 32 (1980), 325–329.MathSciNetCrossRefMATHGoogle Scholar
  21. [Li] Li, P.: On the Sobolev constant and the p-spectrum of a compact Riemannian manifold. Ann. Sc. E.N.S. Paris, 13 (1980), 451–469.MathSciNetMATHGoogle Scholar
  22. [LT] Lu, S. and Tian, G.: To appear.Google Scholar
  23. [Ma] Mabuchi, T.: K-energy maps integrating Futaki invariants. Tohoku Math. J., 38 (1986), 245–257.MathSciNetCrossRefMATHGoogle Scholar
  24. [Mat] Matsushima, Y.: Sur la structure du group d’homeomorphismes analytiques d’une certaine varietie Kaehleriennes, Nagoya Math. J., 11 (1957), 145–150.MathSciNetMATHGoogle Scholar
  25. [Md] Mumford, D.: Stability of projective varieties. L’Enseignement mathématique, II e série, tome 23 (1977), fasc. 1–2.Google Scholar
  26. [Mi] Miyaoka, Y.: On the Chern numbers of surfaces of general type, Inv. math., 32 (1977), 200–312.MathSciNetMATHGoogle Scholar
  27. [Na] Nadel, A.: Multiplier ideal sheaves and existence of Kähler-Einstein metrics of positive scalar curvature. Proc. Natl. Acad. Sci. USA, Vol. 86, No. 19 (1989).Google Scholar
  28. [Si] Sugiyama, K.: On the tangent sheaves of minimal varieties, Kähler Metrics and Moduli Spaces, Adv. Studies in Pure Math., vol. 18, no. 2 (1990).Google Scholar
  29. [T1] Tian, G.: On Kähler-Einstein metrics on certain Kähler Manifolds with C 1 (M)>0 Invent. Math., 89 (1987), 225–246.MathSciNetCrossRefMATHGoogle Scholar
  30. [T2] Tian, G.: On Calabi’s Conjecture for Complex Surfaces with Positive First Chern Class. Inv. Math. Vol. 101, No. 1 (1990), 101–172.CrossRefMATHGoogle Scholar
  31. [T3] Tian, G.: On stability of the tangent bundle of Fano varieties, Journal of International Mathematics, Vol. 3, no. 3 (1992).Google Scholar
  32. [T4] Tian, G.: The K-energy on Hypersurfaces and Stability. Communications in Geometry and Analysis, 1994.Google Scholar
  33. [T5] Tian, G.: Kähler metrics on algebraic manifolds. Harvard thesis, 1988.Google Scholar
  34. [T6] Tian, G.: On the existence of the solutions of a class of real Monge-Ampere equations, Acta Math. Sinica, 1988.Google Scholar
  35. [Ts1] Tsuji, H.: Stability of tangent bundles of minimal algebraic varieties. Topology, 27 (1988), 429–442.MathSciNetCrossRefMATHGoogle Scholar
  36. [Ts2] Tsuji, H.: An inequality of Chern numbers for open varieties. Math. Ann., vol. 277 no. 3 (1987), 483–487.MathSciNetCrossRefMATHGoogle Scholar
  37. [TY1] Tian, G. and Yau, S.T.: Existence of Kähler-Einstein metrics on complete Kähler manifolds and their applications to algebraic geometry. Math Aspects of String Theory, edited by Yau, 574–628, World Sci. Publishing Co. Singapore, 1987.MATHGoogle Scholar
  38. [TY2] Tian, G. and Yau, S.T.: Complete Kahler manifolds with zero Ricci curvature, I. Journal of American Mathematical Society, Vol. 3, no. 3 (1990).Google Scholar
  39. [TY3] Tian, G. and Yau, S.T.: Complete Kähler Manifolds with Zero Ricci Curvature, II. Inventiones Mathematicae, Vol. 106 (1991).Google Scholar
  40. [TY4] Tian, G. and Yau, S.T.: Kähler-Einstein metrics on complex surfaces with C 1 (M) positive. Comm. Math. Phys., 112 (1987).Google Scholar
  41. [Vi] Viehweg, E.: Weak Positivity and Stability of certain Hilbert Points. Inv. Math., Part I, 96 (1989) 639–667; Part II, 101 (1990), 191–223.MathSciNetCrossRefMATHGoogle Scholar
  42. [Y1] Yau, S.T.: On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampére equation, I *. Comm. Pure Appl. Math., 31 (1978), 339–441.MathSciNetCrossRefMATHGoogle Scholar
  43. [Y2] Yau, S.T.: On Calabi’s conjecture and some new results in algebraic geometry. Proc. Nat. Acad. Sci. USA 74 (1977), 1798–1799.CrossRefMATHGoogle Scholar
  44. [Y3] Yau, S.T.: A splitting theorem and algebraic geometric characterization of locally Hermitian symmetric spaces. Communication in Analysis and Geometry, vol. 1, no. 3 (1993), 473–486.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Gang Tian
    • 1
  1. 1.Courant Institute of Mathematical SciencesNew York University

Personalised recommendations