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}
}
  • G. Tian, S. Yau
  • Published 1 December 1991
  • Mathematics
  • Inventiones mathematicae
View on Springer
200 Citations
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49
Methods Citations
18
Results Citations
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200 Citations

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References

SHOWING 1-10 OF 14 REFERENCES
Monge-Ampere equations, the Bergman kernel, and geometry of pseudoconvex domains*
On Compact Kahler Manifolds with Positive Definite Ricci Tensor
On the Imbedding of V-Manifolds in Projective Space
Complete Kähler manifolds with zero Ricci curvature. I
On the existence of a complete Kähler metric on non‐compact complex manifolds and the regularity of fefferman's equation
Kähler-Einstein metrics on complex surfaces withC1>0
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…
Groups of polynomial growth and expanding maps
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
Lectures on Geometric Measure Theory
Vanishing Theorems on Complex Manifolds
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