On complete gradient shrinking Ricci solitons
Differential Geometry
2011-02-09 v2
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.
Cite
@article{arxiv.0903.3932,
title = {On complete gradient shrinking Ricci solitons},
author = {Huai-Dong Cao and Detang Zhou},
journal= {arXiv preprint arXiv:0903.3932},
year = {2011}
}
Comments
Theorem 1.2 improved; Corollary 1.1 added