International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 758531, 14 pages
doi:10.1155/2010/758531
Research Article

A Volume Comparison Estimate with Radially Symmetric Ricci Curvature Lower Bound and Its Applications

Zisheng Hu,1 Yadong Jin,2 and Senlin Xu3

1School of Mathematics and Computational Science, Shenzhen University, Shenzhen, Guangdong 518060, China
2School of Mathematics and Physics, Jiangsu Teachers University of Technology, Changzhou, Jiangsu 213001, China
3Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China

Received 3 July 2009; Revised 16 October 2009; Accepted 17 February 2010

Academic Editor: Mircea-Eugen Craioveanu

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.

Abstract

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.