Bounding scalar curvature for global solutions of the Kähler-Ricci flow

Jian Song, Gang Tian

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

We show that the scalar curvature is uniformly bounded for the normalized Kähler-Ricci flow on a Kähler manifold with semi-ample canonical bundle. In particular, the normalized Kähler- Ricci flow has long time existence if and only if the scalar curvature is uniformly bounded, for Kähler surfaces, projective manifolds of complex dimension three, and for projective manifolds of all dimensions if assuming the abundance conjecture.

Original languageEnglish (US)
Pages (from-to)683-695
Number of pages13
JournalAmerican Journal of Mathematics
Volume138
Issue number3
DOIs
StatePublished - Jun 2016

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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