On the weighted forward reduced volume of Ricci flow

Cheng, Liang; Zhu, Anqiang

doi:10.1090/S0002-9939-2013-11687-4

On the weighted forward reduced volume of Ricci flow
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by Liang Cheng and Anqiang Zhu PDF

Proc. Amer. Math. Soc. 141 (2013), 2859-2868 Request permission

Abstract:

In this paper, we introduce the weighted forward reduced volume of Ricci flow. The weighted forward reduced volume, which is related to expanders of Ricci flow, is well-defined on noncompact manifolds and monotone nonincreasing under Ricci flow. Moreover, we show that, just the same as Perelman’s reduced volume, the weighted reduced volume entropy has the value $(4\pi )^{\frac {n}{2}}$ if and only if the Ricci flow is the trivial flow on flat Euclidean space.

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