Kähler-Einstein metrics on complex surfaces with C1>0

Gang Tian, Shing Tung Yau

Research output: Contribution to journalArticlepeer-review

167 Scopus citations


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 languageEnglish (US)
Pages (from-to)175-203
Number of pages29
JournalCommunications In Mathematical Physics
Issue number1
StatePublished - Mar 1987

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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