Kähler-Einstein metrics on algebraic manifolds

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


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  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

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