Kähler-Einstein metrics with positive scalar curvature |
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Authors: | Gang Tian |
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Institution: | (1) Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Má 02139-4307, USA (e-mail: tian@math.mit.edu), US |
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Abstract: | In this paper, we prove that the existence of K?hler-Einstein metrics implies the stability of the underlying K?hler manifold
in a suitable sense. In particular, this disproves a long-standing conjecture that a compact K?hler manifold admits K?hler-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 K?hler-Einstein metrics. Our arguments also yield that the analytic criterion is satisfied
on stable K?hler manifolds, provided that the partial C
0-estimate posed in T6] is true.
Oblatum 12-IV-1996 & 8-XI-1996 |
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Keywords: | |
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