### 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 with C_{1}>0, in particular, we prove that there are Kähler-Einstein structures with C_{1}>0 on any manifold of differential type {Mathematical expression}.

Original language | English (US) |
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Pages (from-to) | 175-203 |

Number of pages | 29 |

Journal | Communications in Mathematical Physics |

Volume | 112 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 1987 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Tian, G., & Yau, S. T. (1987). Kähler-Einstein metrics on complex surfaces with C

_{1}>0.*Communications in Mathematical Physics*,*112*(1), 175-203. https://doi.org/10.1007/BF01217685