Kähler-Einstein metrics with positive scalar curvature

Gang Tian

Research output: Contribution to journalArticlepeer-review

528 Scopus citations


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 C0-estimate posed in [T6] is true.

Original languageEnglish (US)
Pages (from-to)1-37
Number of pages37
JournalInventiones Mathematicae
Issue number1
StatePublished - Oct 1997

All Science Journal Classification (ASJC) codes

  • General Mathematics


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