Open manifolds with asymptotically nonnegative Ricci curvature and large volume growth

Yuntao Zhang

Open manifolds with asymptotically nonnegative Ricci curvature and large volume growth

Differential Geometry 2014-08-19 v1

Authors: Yuntao Zhang

Abstract

In this paper, we study the topology of complete noncompact Riemannian manifolds with asymptotically nonnegative Ricci curvature and large volume growth. We prove that they have finite topological types under some curvature decay and volume growth conditions. We also generize it to the manifolds with $k$ -th asymptotically nonnegative Ricci curvature by using extensions of Abresch-Gromoll's excess function estimate.

Keywords

open manifolds Ricci curvature volume growth topological type Abresch-Gromoll excess function Riemannian manifolds

Cite

@article{arxiv.1408.3882,
  title  = {Open manifolds with asymptotically nonnegative Ricci curvature and large volume growth},
  author = {Yuntao Zhang},
  journal= {arXiv preprint arXiv:1408.3882},
  year   = {2014}
}

Comments

11 pages

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