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On a Sharp Volume Estimate for Gradient Ricci Solitons with Scalar Curvature Bounded Below 被引量:2
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作者 shi jin zhang 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第5期871-882,共12页
In this note, we obtain a sharp volume estimate for complete gradient Ricci solitons with scalar curvature bounded below by a positive constant. Using Chen-Yokota's argument we obtain a local lower bound estimate of ... In this note, we obtain a sharp volume estimate for complete gradient Ricci solitons with scalar curvature bounded below by a positive constant. Using Chen-Yokota's argument we obtain a local lower bound estimate of the scalar curvature for the Ricci flow on complete manifolds. Consequently, one has a sharp estimate of the scalar curvature for expanding Ricci solitons; we also provide a direct (elliptic) proof of this sharp estimate. Moreover, if the scalar curvature attains its minimum value at some point, then the manifold is Einstein. 展开更多
关键词 Ricci solitons Einstein manifold scalar curvature
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