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arXiv · 1111.4013

On the Perelman's reduced entropy and Ricci flat manifolds with maximal volume growth

Liang Cheng·Anqiang Zhu
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Abstract

In this paper, we study the Ricci flat manifolds with maximal volume growth using Perelman's reduced volume of Ricci flow. We show that if $(M^n,g)$ is an noncompact complete Ricci flat manifold with maximal volume growth satisfying $|Rm|(x)\to 0$ as $d(x)=d_g(x,p)\to \infty$, then $M^n$ has the quadratic curvature decay. Some applications to this result are also presented.

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Liang Cheng, Anqiang Zhu. 2011-11-17. On the Perelman's reduced entropy and Ricci flat manifolds with maximal volume growth. https://arxiv.org/abs/1111.4013

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