The J-flow on Kähler surfaces: A boundary case

Hao Fang, Mijia Lai, Jian Song, Ben Weinkove

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We study the J-flow on Kähler surfaces when the Kähler class lies on the boundary of the open cone for which global smooth convergence holds and satisfies a nonnegativity condition. We obtain a C0 estimate and show that the J-flow converges smoothly to a singular Kähler metric away from a finite number of curves of negative self-intersection on the surface. We discuss an application to the Mabuchi energy functional on Kähler surfaces with ample canonical bundle.

Original languageEnglish (US)
Pages (from-to)215-226
Number of pages12
JournalAnalysis and PDE
Volume7
Issue number1
DOIs
StatePublished - 2014

Keywords

  • Complex monge-ampère
  • J-flow
  • Kähler

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

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