Harnack Estimates for Ricci Flow on a Warped Product

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Abstract

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
Volume26
Issue number3
DOIs
StatePublished - Jul 1 2016

Keywords

  • Harnack estimates
  • Ricci flow
  • Warped product

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