International Journal of Mathematics and Mathematical Sciences (Jan 2010)

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

  • Zisheng Hu,
  • Yadong Jin,
  • Senlin Xu

DOI
https://doi.org/10.1155/2010/758531
Journal volume & issue
Vol. 2010

Abstract

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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.