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

Research output: Contribution to journal › Article › peer-review

152 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

Access to Document

10.1007/BF01217685

Cite this

@article{3c25e72a7f4b4e6c8f3fa0057a1bb7d0,

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}.",

author = "Gang Tian and Yau, {Shing Tung}",

year = "1987",

month = mar,

day = "1",

doi = "10.1007/BF01217685",

language = "English (US)",

volume = "112",

pages = "175--203",

journal = "Communications in Mathematical Physics",

issn = "0010-3616",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Kähler-Einstein metrics on complex surfaces with C1>0

AU - Tian, Gang

AU - Yau, Shing Tung

PY - 1987/3/1

Y1 - 1987/3/1

N2 - 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}.

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}.

UR - http://www.scopus.com/inward/record.url?scp=0001120933&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001120933&partnerID=8YFLogxK

U2 - 10.1007/BF01217685

DO - 10.1007/BF01217685

M3 - Article

AN - SCOPUS:0001120933

VL - 112

SP - 175

EP - 203

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -

Kähler-Einstein metrics on complex surfaces with C₁>0

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this