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arXiv · 0903.3932

On complete gradient shrinking Ricci solitons

Huai-Dong Cao·Detang Zhou
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Abstract

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.

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Huai-Dong Cao, Detang Zhou. 2009-03-23. On complete gradient shrinking Ricci solitons. https://arxiv.org/abs/0903.3932

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