Open manifolds with asymptotically nonnegative Ricci curvature and large volume growth

Zhang, Yuntao

doi:10.1090/proc12787

Open manifolds with asymptotically nonnegative Ricci curvature and large volume growth
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Proc. Amer. Math. Soc. 143 (2015), 4913-4923 Request permission

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 generalize it to the manifolds with $k$th asymptotically nonnegative Ricci curvature by using extensions of Abresch-Gromoll’s excess function estimate.

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