Japanese Journal of Mathematics

, Volume 10, Issue 1, pp 1–41

Kähler–Einstein metrics on Fano manifolds

Special Feature: The Takagi Lectures

DOI: 10.1007/s11537-014-1387-3

Cite this article as:
Tian, G. Jpn. J. Math. (2015) 10: 1. doi:10.1007/s11537-014-1387-3


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.

Keywords and phrases

Kähler–Einstein metrics manifold Futaki invariant K-stability partial C0-estimate 

Mathematics Subject Classification (2010)

58 53 14 

Copyright information

© The Mathematical Society of Japan and Springer Japan 2014

Authors and Affiliations

  1. 1.Beijing International Center for Mathematical ResearchPeking UniversityBeijingP.R. China
  2. 2.Princeton UniversityPrincetonUSA