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

2011/11/17 by Cheng, Liang, Zhu, Anqiang · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1111.4013

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 (Mⁿ,g) is an noncompact complete Ricci flat manifold with maximal volume growth satisfying |Rm|(x)→ 0 as d(x)=d_g(x,p)→ ∞, then Mⁿ has the quadratic curvature decay. Some applications to this result are also presented.

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