Abstract
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.
Citation
Huai-Dong Cao. Detang Zhou. "On complete gradient shrinking Ricci solitons." J. Differential Geom. 85 (2) 175 - 186, June 2010. https://doi.org/10.4310/jdg/1287580963
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