Open Access
June 2010 On complete gradient shrinking Ricci solitons
Huai-Dong Cao, Detang Zhou
J. Differential Geom. 85(2): 175-186 (June 2010). DOI: 10.4310/jdg/1287580963


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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Huai-Dong Cao. Detang Zhou. "On complete gradient shrinking Ricci solitons." J. Differential Geom. 85 (2) 175 - 186, June 2010.


Published: June 2010
First available in Project Euclid: 20 October 2010

zbMATH: 1246.53051
MathSciNet: MR2732975
Digital Object Identifier: 10.4310/jdg/1287580963

Rights: Copyright © 2010 Lehigh University

Vol.85 • No. 2 • June 2010
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