Harnack Estimates for Ricci Flow on a Warped Product

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In this paper, we study the Ricci flow on a closed manifold equipped with a warped product metric (N× F, gN+ f2gF) in which (F, gF) is Ricci flat. Using the framework of monotone formulas, we derive several estimates for the adapted heat conjugate fundamental solution which include an analog of Perelman’s differential Harnack inequality (The entropy formula for the Ricci flow and its geometric applications, 2002).

Original languageEnglish
Pages (from-to)1838-1862
Number of pages25
JournalJournal of Geometric Analysis
Issue number3
StatePublished - Jul 1 2016


  • Harnack estimates
  • Ricci flow
  • Warped product


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