Bounding scalar survature and diameter along the Kähler Ricci flow (after Perelman)

Natasa Sesum, Gang Tian

Research output: Contribution to journalArticlepeer-review

109 Scopus citations


In this short note we present a result of Perelman with detailed proof. The result states that if g(t) is the Kähler Ricci flow on a compact, Kähler manifold M with c1 (M) > 0, the scalar curvature and diameter of (M, g(t)) stay uniformly bounded along the flow, for t ∈ [0, infin;). We learned about this result and its proof from Grigori Perelman when he was visiting MIT in the spring of 2003. This may be helpful to people studying the Kähler Ricci flow.

Original languageEnglish (US)
Pages (from-to)575-587
Number of pages13
JournalJournal of the Institute of Mathematics of Jussieu
Issue number3
StatePublished - Jul 2008

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • Diameter
  • Kähler Ricci flow
  • Scalar curvature


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