On the asymptotic reduced volume of the Ricci flow

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4 Citations (Scopus)


In this article, we consider two different monotone quantities defined for the Ricci flow and show that their asymptotic limits coincide for any ancient solutions. One of the quantities we consider here is Perelman's reduced volume, while the other is the local quantity discovered by Ecker, Knopf, Ni, and Topping. This establishes a relation between these two monotone quantities.

Original languageEnglish
Pages (from-to)263-274
Number of pages12
JournalAnnals of Global Analysis and Geometry
Issue number3
Publication statusPublished - 2010 Mar
Externally publishedYes


  • Ancient solution
  • Monotonicity formula
  • Reduced volume
  • Ricci flow

ASJC Scopus subject areas

  • Analysis
  • Political Science and International Relations
  • Geometry and Topology


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