On complete gradient shrinking Ricci solitons
On complete gradient shrinking Ricci solitons
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DOI：
10.4310/jdg/1287580963
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发表时间：
2009-03
期刊：
影响因子：
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通讯作者：
H. Cao;Detang Zhou
中科院分区：
文献类型：
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作者：
H. Cao;Detang Zhou
本文给出了完全非紧收缩孤子势函数增长性的精确估计。在此基础上，我们证明了一个完全的非紧梯度收缩Ricci孤子至多具有欧氏体积增长。后一个结果可以被看作是著名的Bishop定理的类比，即具有非负Ricci曲率的完备非紧黎曼流形至多具有欧几里得体积增长。
In this paper we derive a precise estimate on the growth of potential functions of complete noncompact shrinking solitons. Based on this, we prove that a complete noncompact gradient shrinking Ricci soliton has at most Euclidean volume growth. The latter result can be viewed as an analog of the well-known theorem of Bishop that a complete noncompact Riemannian manifold with nonnegative Ricci curvature has at most Euclidean volume growth.