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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 {pipe}Rm{pipe}(x)→ 0 as d(x) = dg(x,p) → ∞,then Mn has the quadratic curvature decay. Some applications to this result are also presented. © 2012 Springer-Verlag Berlin Heidelberg.

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