On the convergence of the modified Kähler-Ricci flow and solitons

D. H. Phong, Jian Song, Jacob Sturm, Ben Weinkove

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


We investigate the Kähler-Ricci flow modified by a holomorphic vector field. We find equivalent analytic criteria for the convergence of the flow to a Kähler-Ricci soliton. In addition, we relate the asymptotic behavior of the scalar curvature along the flow to the lower boundedness of the modified Mabuchi energy.

Original languageEnglish (US)
Pages (from-to)91-112
Number of pages22
JournalCommentarii Mathematici Helvetici
Issue number1
StatePublished - 2011


  • Hler-Ricci flow
  • Mabuchi energy
  • Soliton

ASJC Scopus subject areas

  • Mathematics(all)

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