Convergence of the J-flow on Kähler surfaces

Ben Weinkove*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

35 Scopus citations

Abstract

Donaldson defined a parabolic flow of potentials on Kähler manifolds which arises from considering the action of a group of symplectomorphisms on the space of smooth maps between manifolds. One can define a moment map for this action, and then consider the gradient flow of the square of its norm. Chen discovered the same flow from a different viewpoint and called it the J-flow, since it corresponds to the gradient flow of his J-functional, which is related to Mabuchi's K-energy. In this paper, we show that in the case of Kähler surfaces with two Kähler forms satisfying a certain inequality, the J-flow converges to a zero of the moment map.

Original languageEnglish (US)
Pages (from-to)949-965
Number of pages17
JournalCommunications in Analysis and Geometry
Volume12
Issue number4
DOIs
StatePublished - Oct 2004

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Geometry and Topology
  • Statistics, Probability and Uncertainty

Fingerprint Dive into the research topics of 'Convergence of the J-flow on Kähler surfaces'. Together they form a unique fingerprint.

Cite this