Volume Growth and the Topology of Manifolds with Nonnegative Ricci Curvature

@article{Munn2007VolumeGA,
  title={Volume Growth and the Topology of Manifolds with Nonnegative Ricci Curvature},
  author={Michael Munn},
  journal={Journal of Geometric Analysis},
  year={2007},
  volume={20},
  pages={723-750}
}
Let Mn be a complete, open Riemannian manifold with Ric≥0. In 1994, Grigori Perelman showed that there exists a constant δn>0, depending only on the dimension of the manifold, such that if the volume growth satisfies $\alpha_{M}:=\lim_{r\rightarrow \infty}\frac{\operatorname{Vol}(B_{p}(r))}{\omega_{n}r^{n}}\geq 1-\delta_{n}$, then Mn is contractible. Here we employ the techniques of Perelman to find specific lower bounds for the volume growth, α(k,n), depending only on k and n, which guarantee… CONTINUE READING

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