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

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.