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Open manifolds with asymptotically nonnegative Ricci curvature and large volume growth


Author: Yuntao Zhang
Journal: Proc. Amer. Math. Soc. 143 (2015), 4913-4923
MSC (2010): Primary 53C20; Secondary 53C21
DOI: https://doi.org/10.1090/proc12787
Published electronically: July 15, 2015
MathSciNet review: 3391049
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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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Additional Information

Yuntao Zhang
Affiliation: School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, People’s Republic of China
Email: yuntaozhang@jsnu.edu.cn

DOI: https://doi.org/10.1090/proc12787
Keywords: Ricci curvature, finite topological type, volume growth
Received by editor(s): August 14, 2014
Received by editor(s) in revised form: August 15, 2014
Published electronically: July 15, 2015
Additional Notes: This work was supported by PAPD of Jiangsu Higher Education Institutions.
Communicated by: Lei Ni
Article copyright: © Copyright 2015 American Mathematical Society