Inventiones mathematicae

, Volume 130, Issue 1, pp 1–37 | Cite as

Kähler-Einstein metrics with positive scalar curvature

  • Gang Tian


In this paper, we prove that the existence of Kähler-Einstein metrics implies the stability of the underlying Kähler manifold in a suitable sense. In particular, this disproves a long-standing conjecture that a compact Kähler manifold admits Kähler-Einstein metrics if it has positive first Chern class and no nontrivial holomorphic vector fields. We will also establish an analytic criterion for the existence of Kähler-Einstein metrics. Our arguments also yield that the analytic criterion is satisfied on stable Kähler manifolds, provided that the partial C 0-estimate posed in [T6] is true.


Manifold Vector Field Analytic Criterion Scalar Curvature Chern Class 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Gang Tian
    • 1
  1. 1.Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MÁ 02139-4307, USA (e-mail:

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