On the asymptotic reduced volume of the Ricci flow

Details On the asymptotic reduced volume of the Ricci flow On the asymptotic reduced volume of the Ricci flow

2009-04-06

arxiv.org/abs/0904.0868v1

Mathematics

Differential Geometry

12 pages

Scientific paper

In this paper, 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.

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