TY - CHAP
T1 - Existence of Einstein metrics on Fano manifolds
AU - Tian, Gang
N1 - Publisher Copyright:
© Springer Basel 2012.
PY - 2012
Y1 - 2012
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
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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 -