Perelman's reduced volume and a gap theorem for the Ricci flow
Perelman's reduced volume and a gap theorem for the Ricci flow
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DOI：
10.4310/cag.2009.v17.n2.a3
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发表时间：
2008-08
期刊：
影响因子：
--
通讯作者：
Takumi Yokota
中科院分区：
文献类型：
--
作者：
Takumi Yokota
在这篇文章中，我们证明了具有约化体积的Ricci流的任何古解，其渐近极限充分接近于高斯孤子的渐近极限，在所有时间都等距于欧几里德空间。这是Anderson关于Ricci-平坦流形的结果的推广。作为推论，还得到了梯度收缩Ricci孤子的间隙定理。
In this paper, we show that any ancient solution to the Ricci flow with the reduced volume whose asymptotic limit is sufficiently close to that of the Gaussian soliton is isometric to the Euclidean space for all time. This is a generalization of Anderson's result for Ricci-flat manifolds. As a corollary, a gap theorem for gradient shrinking Ricci solitons is also obtained.