Annals of Global Analysis and Geometry

, Volume 37, Issue 3, pp 263-274

First online:

On the asymptotic reduced volume of the Ricci flow

  • Takumi YokotaAffiliated withGraduate School of Pure and Applied Sciences, University of Tsukuba Email author 

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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.


Ricci flow Reduced volume Ancient solution Monotonicity formula

Mathematics Subject Classification (2000)

53C21 (primary) 35B40 58J35