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活动类型：研究生课程

主讲人：杨晓奎

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Title： The Existence of Kahler Metrics with Constant Scalar Curvatrue

Abstract：In this seminar, we will introduce some results about the existence of Kahler-Einstein metrics with constant scalar curvature on compact Kahler manifold.  We organize these as follow:

1. In this section we will introduce the fundamental concepts and theorems in Kahler geometry very quickly(including some Hodge theory and the extremal Kahler metrics) and give a presentation of the main topics in section 2 and section 3.

2. In this section we will give a complete proof of Calabi conjecture first obtained by S.T.Yau in 1977. We will add some detail about the computation.

3. In this section we will introduce the work of A.Futaki, especially his famous integral invariants--futaki invariants and the later generalization by Bando.

4. In this section we will introduction some other results about Kahler- Einstein metrics including some important results obtained by T.Aubin, K.F.Liu, Y.Matsushima, Y.T.Siu, G.Tian, S.T.Yau and etc.

"Maybe" I will give some  presentation of S.K.Donaldson's work about the exisitence of Kahler-Eistein metrics with constant scalar curvature at the end the August.
 
PS: Maybe at the end of my sections some expert about Donaldson's work will come to hangzhou. We will invite him to give us some lectures if it's possible.

The Main References:
1. S.K. Donaldson, Scalar Curvature and the stability of toric varieties, JDG 62(2002)  289-349.
2. A.Futaki, An obstruction to the existence of Kahler-Einstein Metrics. Invent. Math. 73, 437-443 (1983)
3. A. Futaki, Kahler-Einstein Metrics and Integral Invariants. LNM 1341.
4. G.Tian, Canonical Metrics in Kahler Geometry.  Lectures in Mathematics ETH Zurich.
5. S.T.Yau,  On the Ricci-Curvature of a Complex Kahler Manifold and the Complex Monge-Apere Equations. Commun.Pure Appl. Math,31,339-411 (1978)