Annals of Global Analysis and Geometry

, Volume 37, Issue 3, pp 263–274

On the asymptotic reduced volume of the Ricci flow

Authors

    • Graduate School of Pure and Applied SciencesUniversity of Tsukuba
Article

DOI: 10.1007/s10455-009-9184-6

Cite this article as:
Yokota, T. Ann Glob Anal Geom (2010) 37: 263. doi:10.1007/s10455-009-9184-6
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Abstract

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.

Keywords

Ricci flowReduced volumeAncient solutionMonotonicity formula

Mathematics Subject Classification (2000)

53C21 (primary)35B4058J35

Copyright information

© Springer Science+Business Media B.V. 2009