A necessary and sufficient condition for Ricci shrinkers to have   positive AVR
  In this short note we observe that a recent result of C.-W. Chen meshes well with earlier work of H.-D. Cao and D.-T. Zhou, O. Munteanu, J. Carrillo and L. Ni, and S.-J. Zhang to give a necessary and sufficient condition for complete noncompact shrinking gradient Ricci solitons to have positive asymptotic volume ratio. 
Bennett Chow, Peng Lu and Bo Yang
math.DG