# Complete Kähler manifolds with zero Ricci curvature II

@article{Tian1991CompleteKM,
title={Complete K{\"a}hler manifolds with zero Ricci curvature II},
author={Gang Tian and Shing-Tung Yau},
journal={Inventiones mathematicae},
year={1991},
volume={106},
pages={27-60}
}
• Published 1 December 1991
• Mathematics
• Inventiones mathematicae
201 Citations
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## References

SHOWING 1-10 OF 14 REFERENCES
Kähler-Einstein metrics on complex surfaces withC1>0
• Mathematics
• 1987
AbstractVarious 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
On Kähler-Einstein metrics on certain Kähler manifolds withC1 (M)>0
On demontre qu'il existe une metrique de Kahler-Einstein sur une hypersurface de Fermat a m dimensions de degre superieur a m-1