Estimates for the complex monge-ampère equation on hermitian and balanced manifolds

Valentino Tosatti*, Ben Weinkove

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

49 Scopus citations

Abstract

We generalize Yau's estimates for the complex Monge-Ampère equation on compact manifolds in the case when the background metric is no longer Kähler. We prove C a priori estimates for a solution of the complex Monge-Ampère equation when the background metric is Hermitian (in complex dimension two) or balanced (in higher dimensions), giving an alternative proof of a theorem of Cherrier. We relate this to recent results of Guan-Li.

Original languageEnglish (US)
Pages (from-to)19-40
Number of pages22
JournalAsian Journal of Mathematics
Volume14
Issue number1
DOIs
StatePublished - Mar 2010

Keywords

  • Balanced manifold
  • Complex Monge-Ampère equation
  • Hermitian manifold

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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