Abstract
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 CO-estimates and their variations. I will also discuss some related problems as well as some recent advances.
Mathematics Subject Classification (2000). 14Jxx, 58Jxx
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Tian, G. (2012). Existence of Einstein Metrics on Fano Manifolds. In: Dai, X., Rong, X. (eds) Metric and Differential Geometry. Progress in Mathematics, vol 297. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0257-4_5
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DOI: https://doi.org/10.1007/978-3-0348-0257-4_5
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