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

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

2011-11-17

arxiv.org/abs/1111.4013v2

Mathematics

Differential Geometry

9 pages

Scientific paper

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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