Perelman's entropy and Kähler-Ricci flow on a Fano manifold

Gang Tian, Shijin Zhang, Zhenlei Zhang, Xiaohua Zhu

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


In this paper, we extend the method in a recent paper of Tian and Zhu to study the energy level L(·) of Perelman's entropy λ(·) for the Kähler-Ricci flow on a Fano manifold M. We prove that L(·) is independent of the initial metric of the Kähler-Ricci flow under an assumption that the modified Mabuchi's K-energy is bounded from below on M. As an application of the above result, we give an alternative proof to the main theorem about the convergence of Kähler-Ricci flow found in a 2007 paper by Tian and Zhu.

Original languageEnglish (US)
Pages (from-to)6669-6695
Number of pages27
JournalTransactions of the American Mathematical Society
Issue number12
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


  • Kähler-Ricci flow
  • Kähler-Ricci solitons
  • Perelman's entropy


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