Abstract
Various estimates of the lower bound of the holomorphic invariant α(M), defined in [T], are given here by using branched coverings, potential estimates and Lelong numbers of positive,d-closed (1, 1) currents of certain type, etc. These estimates are then applied to produce Kähler-Einstein metrics on complex surfaces withC 1>0, in particular, we prove that there are Kähler-Einstein structures withC 1>0 on any manifold of differential type\(CP^2 \# \overline {nCP^2 } (3 \leqq n \leqq 8)\).
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Communicated by E. Lieb
Dedicated to Walter Thirring on his 60th birthday
Research supported in part by Alfred P. Sloan Fellowship for doctoral dissertation
Research supported in part by NSF grant # DMS 84-08447 and ONR contract # N-00014-85-K-0367
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Tian, G., Yau, ST. Kähler-Einstein metrics on complex surfaces withC 1>0. Commun.Math. Phys. 112, 175–203 (1987). https://doi.org/10.1007/BF01217685
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DOI: https://doi.org/10.1007/BF01217685