On complete gradient shrinking Ricci solitons

Details On complete gradient shrinking Ricci solitons On complete gradient shrinking Ricci solitons

2009-03-23

arxiv.org/abs/0903.3932v2

J. Differential Geom., 85 (2010), 175-186

Mathematics

Differential Geometry

Theorem 1.2 improved; Corollary 1.1 added

Scientific paper

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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