Kähler-Einstein metrics on complex surfaces with C1>0

Gang Tian; Shing Tung Yau

doi:10.1007/BF01217685

Kähler-Einstein metrics on complex surfaces with C₁>0

Gang Tian, Shing Tung Yau

Mathematics

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155 Scopus citations

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 C₁>0, in particular, we prove that there are Kähler-Einstein structures with C₁>0 on any manifold of differential type {Mathematical expression}.

Original language	English (US)
Pages (from-to)	175-203
Number of pages	29
Journal	Communications in Mathematical Physics
Volume	112
Issue number	1
DOIs	https://doi.org/10.1007/BF01217685
State	Published - Mar 1 1987

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01217685

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title = "K{\"a}hler-Einstein metrics on complex surfaces with C1>0",

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 K{\"a}hler-Einstein metrics on complex surfaces with C1>0, in particular, we prove that there are K{\"a}hler-Einstein structures with C1>0 on any manifold of differential type {Mathematical expression}.",

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year = "1987",

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AB - 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 C1>0, in particular, we prove that there are Kähler-Einstein structures with C1>0 on any manifold of differential type {Mathematical expression}.

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Kähler-Einstein metrics on complex surfaces with C₁>0

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