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arXiv · 1011.0504

On the weighted forward reduced Entropy of Ricci flow

Liang Cheng·Anqiang Zhu
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Abstract

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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Liang Cheng, Anqiang Zhu. 2010-11-02. On the weighted forward reduced Entropy of Ricci flow. https://arxiv.org/abs/1011.0504

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