Bounds on volume growth of geodesic balls under Ricci flow
Bounds on volume growth of geodesic balls under Ricci flow
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DOI：
10.4310/mrl.2012.v19.n1.a19
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发表时间：
2011-07
期刊：
影响因子：
--
通讯作者：
Qi S. Zhang
中科院分区：
文献类型：
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作者：
Qi S. Zhang
我们证明了一个所谓的$\kappa$非膨胀性质的Ricci流，它提供了一个上界的体积比的测地球超过欧氏的，下一个上界的标量曲率。这一结果可以看作是Perelman关于Ricci流的$\kappa$非坍缩性质的相反陈述。这两个结果共同暗示了Ricci流的体积加倍性质，而不需要假设Ricci曲率的下界。
We prove a so called $\kappa$ non-inflating property for Ricci flow, which provides an upper bound for volume ratio of geodesic balls over Euclidean ones, under an upper bound for scalar curvature. This result can be regarded as the opposite statement of Perelman's $\kappa$ non-collapsing property for Ricci flow. These two results together imply volume doubling property for Ricci flow without assuming Ricci curvature lower bound.