Kähler–Einstein metrics on Fano manifolds

Gang Tian

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5 Scopus citations


This is an expository paper on Kähler metrics of positive scalar curvature. It is for my Takagi Lectures at RIMS in November of 2013. In this paper, I first discuss the Futaki invariants, the K-stability and its relation to the K-energy. Next I will outline my work in 2012 on the existence of Kähler–Einstein metrics on K-stable Fano manifolds. Finally, I will present S. Paul’s work on stability of pairs with some modifications of mine.

Original languageEnglish (US)
Pages (from-to)1-41
Number of pages41
JournalJapanese Journal of Mathematics
Issue number1
StatePublished - Mar 2015

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • Futaki invariant
  • K-stability
  • Kähler–Einstein
  • manifold
  • metrics
  • partial C-estimate


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