TY - CHAP

T1 - Existence of Einstein metrics on Fano manifolds

AU - Tian, Gang

PY - 2012/1/1

Y1 - 2012/1/1

N2 - It is a long-standing problem to establish the existence of Kähler-Einstein metrics on Fano manifolds since Yau’s solution for the Calabi conjecture in late 70s. It is also one of driving forces in today’s study in Kähler geometry. In this paper, we discuss a program I started more than twenty years ago on this famous problem. It includes some of my results and speculations on the existence of Kähler-Einstein metrics on Fano manifolds, such as, holomorphic invariants, the K-stability, the compactness theorem for Kähler-Einstein manifolds, the partial C0-estimates and their variations. I will also discuss some related problems as well as some recent advances.

AB - It is a long-standing problem to establish the existence of Kähler-Einstein metrics on Fano manifolds since Yau’s solution for the Calabi conjecture in late 70s. It is also one of driving forces in today’s study in Kähler geometry. In this paper, we discuss a program I started more than twenty years ago on this famous problem. It includes some of my results and speculations on the existence of Kähler-Einstein metrics on Fano manifolds, such as, holomorphic invariants, the K-stability, the compactness theorem for Kähler-Einstein manifolds, the partial C0-estimates and their variations. I will also discuss some related problems as well as some recent advances.

KW - Compactness theorems

KW - Fano manifolds

KW - Holomorphic invariants

KW - K-stability

KW - Kähler-Einstein metrics

UR - http://www.scopus.com/inward/record.url?scp=84991202252&partnerID=8YFLogxK

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U2 - 10.1007/978-3-0348-0257-4_5

DO - 10.1007/978-3-0348-0257-4_5

M3 - Chapter

AN - SCOPUS:84991202252

T3 - Progress in Mathematics

SP - 119

EP - 159

BT - Progress in Mathematics

PB - Springer Basel

ER -