Abstract.
In this paper, we prove that the existence of Kähler-Einstein metrics implies the stability of the underlying Kähler manifold in a suitable sense. In particular, this disproves a long-standing conjecture that a compact Kähler manifold admits Kähler-Einstein metrics if it has positive first Chern class and no nontrivial holomorphic vector fields. We will also establish an analytic criterion for the existence of Kähler-Einstein metrics. Our arguments also yield that the analytic criterion is satisfied on stable Kähler manifolds, provided that the partial C 0-estimate posed in [T6] is true.
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Oblatum 12-IV-1996 & 8-XI-1996
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Tian, G. Kähler-Einstein metrics with positive scalar curvature. Invent math 130, 1–37 (1997). https://doi.org/10.1007/s002220050176
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DOI: https://doi.org/10.1007/s002220050176