Japanese Journal of Mathematics

, Volume 10, Issue 1, pp 1–41 | Cite as

Kähler–Einstein metrics on Fano manifolds

Special Feature: The Takagi Lectures

Abstract

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 

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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

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