  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.
