Kähler–Einstein metrics on Fano manifolds
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- 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.