A Property of K\"{a}hler-Ricci Solitons on Complete Complex Surfaces
  In this paper we prove that a nonflat K\"{a}hler-Ricci soliton of the Ricci flow on a complex two-dimensional K\"{a}hler manifold with nonnegative holomorphic bisectional curvature can not be of maximal volume growth. 
Bing-Long Chen and Xi-Ping Zhu