On the weighted forward reduced Entropy of Ricci flow

Details On the weighted forward reduced Entropy of Ricci flow On the weighted forward reduced Entropy of Ricci flow

2010-11-02

arxiv.org/abs/1011.0504v3

Mathematics

Differential Geometry

10 pages

Scientific paper

In this paper, we first introduce the weighted forward reduced volume of Ricci flow. The weighted forward reduced volume, which related to expanders of Ricci flow, is well-defined on noncompact manifolds and monotone non-increasing under Ricci flow. Moreover, we show that, just the same as the 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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