Copyright © 2010 Zisheng Hu et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We extend the classical Bishop-Gromov volume comparison from constant
Ricci curvature lower bound to radially symmetric Ricci curvature lower bound, and
apply it to investigate the volume growth, total Betti number, and finite topological
type of manifolds with nonasymptotically almost nonnegative Ricci curvature.