The complex monge-ampère equation on some compact hermitian manifolds

Jianchun Chu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We consider the complex Monge-Ampère equation on compact manifolds when the background metric is a Hermitian metric (in complex dimension 2) or a Hermitian metric satisfying an additional condition (in higher dimensions). We prove that the Laplacian estimate holds when F is in W1,q0 for any q0 > 2n. As an application, we show that, up to scaling, there exists a unique classical solution in W3,q0 for the complex Monge-Ampère equation when F is in W1,q0.

Original languageEnglish (US)
Pages (from-to)369-386
Number of pages18
JournalPacific Journal of Mathematics
Volume276
Issue number2
DOIs
StatePublished - 2015

Keywords

  • Compact hermitian manifold
  • Complex monge-ampère equation

ASJC Scopus subject areas

  • Mathematics(all)

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