, Volume 37, Issue 3, pp 263-274
Date: 06 Nov 2009

On the asymptotic reduced volume of the Ricci flow

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.