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

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

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 R...

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Veröffentlicht in:International Journal of Mathematics and Mathematical Sciences 2010, Vol.2010 (2010), p.1062-1075
Hauptverfasser: Hu, Zisheng, Jin, Yadong, Xu, Senlin
Format: Artikel
Sprache:eng
Schlagworte:
Curvature
Estimates
Lower bounds
Manifolds
Mathematical analysis
Studies
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Zusammenfassung: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.
ISSN:0161-1712
1687-0425
DOI:10.1155/2010/758531