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On complete gradient shrinking ricci solitons

Huai-Dong Cao Lehigh University Detang Zhou Universidade Federal Fluminense

Differential Geometry mathscidoc:1609.10181

Journal of Differential Geometry, 85, (2), 175-185, 2010
In this paper we derive optimal growth estimates on the 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. This latter result can be viewed as an analog of the well-known volume comparison theorem of Bishop that a complete noncompact Riemannian manifold with nonnegative Ricci curvature has at most Euclidean volume growth.
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@inproceedings{huai-dong2010on,
  title={ON COMPLETE GRADIENT SHRINKING RICCI SOLITONS},
  author={Huai-Dong Cao, and Detang Zhou},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911215358488792838},
  booktitle={Journal of Differential Geometry},
  volume={85},
  number={2},
  pages={175-185},
  year={2010},
}
Huai-Dong Cao, and Detang Zhou. ON COMPLETE GRADIENT SHRINKING RICCI SOLITONS. 2010. Vol. 85. In Journal of Differential Geometry. pp.175-185. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911215358488792838.
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