Inventiones mathematicae

, Volume 106, Issue 1, pp 27–60

Complete Kähler manifolds with zero Ricci curvature II

  • Gang Tian
  • Shing Tung Yau


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  1. [Ba] Baily, W.: On the imbedding ofV-manifolds in projective space. Am. J. Math.79, 403–430 (1957)Google Scholar
  2. [BK] Bando, S., Kobayashi, R.: Complete Ricci-flat Kähler metrics. (Preprint)Google Scholar
  3. [CY1] Cheng, S.Y., Yau, S.T.: On the existence of complete Kähler metric on noncompact complex manifolds and the regularity of Fefferman's equation. Commun. Pure Appl. Math.33, 507–544 (1980)Google Scholar
  4. [CY2] Cheng, S.Y., Yau, S.T.: Inequality between Chern numbers of singular Kähler surfaces and characterization of orbit space of discrete group of SU (2, 1). Contemp. Math.49, 31–43 (1986)Google Scholar
  5. [Fed] Federer, H.: Geometry Measure Theory. (Grundlehren Math. Wiss., Bd. 153) Berlin Heidelberg New York: Springer 1969Google Scholar
  6. [Fef] Fefferman, C.: Monge-Ampère equations, the Berman kernel, and geometry of pseudoconvex domains. Ann. Math.103, 395–416 (1976)Google Scholar
  7. [Gr] Gromov, M.: Groups of polynomial growth and expanding maps. Publ. Math., Inst. Hautes Étud. Sci.53 (1981)Google Scholar
  8. [GT] Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. Berlin Heidelberg New York: Springer 1977Google Scholar
  9. [Ko] Kobayashi, S.: On compact Kähler manifolds with positive definite Ricci tensor. Ann. Math.74, 570–574 (1961)Google Scholar
  10. [Sh] Shiffman, B.: Vanishing theorems on complex manifolds. (Prog. Math., vol. 56) Basel Boston Stuttgart: Birkhaüser 1985Google Scholar
  11. [Si] Simon, L.: Lectures on geometric measure theory. Proc. Cent. Math. Anal. Aust. Natl. Univ.3 (1983)Google Scholar
  12. [T1] Tian, G.: On Kähler-Einstein metrics on certain Kähler manifolds with C1(M)>0. Invent. Math.89, 225–246 (1987)Google Scholar
  13. [T2] Tian, G.: On Calabi's conjecture for complex surfaces with positive first Chern class. Invent. Math101, 101–172 (1990)Google Scholar
  14. [TY1] Tian, G., Yau, S.T.: Complete Kähler manifolds with zero Ricci curvature. 1. J. Am. Math. Soc.3, 579–610 (1990)Google Scholar
  15. [TY2] Tian, G., Yau, S.T.: Kähler-Einstein metrics on complex surfaces with C1>0. Commun. Math. Phys.112, 175–203 (1987)Google Scholar
  16. [TY3] Tian, G., Yau, S.T.: (Preprint)Google Scholar
  17. [Y1] Yau, S.T.: Isoperimetric constants and the first eigenvalue of a compact Riemannian manifold. Ann. Sci. Éc. Norm. Supér., IV. Sér.8, 487–507 (1975)Google Scholar
  18. [Y2] Yau, S.T.: On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation, I*. Commun. Pure Appl. Math.31, 339–411 (1978)Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Gang Tian
    • 1
  • Shing Tung Yau
    • 2
  1. 1.Institute for Advanced StudySchool of MathematicsPrincetonUSA
  2. 2.Department of MathematicsHarvard UniversityCambridgeUSA

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