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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Large volume growth
and finite topological type


Authors: D. Ordway, B. Stephens and D. G. Yang
Journal: Proc. Amer. Math. Soc. 128 (2000), 1191-1196
MSC (1991): Primary 53C21
DOI: https://doi.org/10.1090/S0002-9939-99-05609-9
Published electronically: December 10, 1999
MathSciNet review: 1705745
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Abstract: It is shown in this paper that a complete noncompact $n$-dimensional Riemannian manifold with nonnegative Ricci curvature, sectional curvature bounded from below, and large volume growth is of finite topological type provided that the volume growth rate of the complement of the cone of rays from a fixed base point is less than $2-1/n$.


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Additional Information

D. Ordway
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02139
Email: ordway@abel.math.harvard.edu

B. Stephens
Email: bstephen@fas.harvard.edu

D. G. Yang
Affiliation: Department of Mathematics, Tulane University, New Orleans, Louisiana 70118
Email: dgy@math.tulane.edu

DOI: https://doi.org/10.1090/S0002-9939-99-05609-9
Keywords: Excess function, finite topological type, large volume growth, nonnegative Ricci curvature, Riemannian manifold, volume comparison theorem
Received by editor(s): January 11, 1998
Published electronically: December 10, 1999
Additional Notes: This research was partially supported by NSF grant DMS97-32058.
Communicated by: Christopher Croke
Article copyright: © Copyright 2000 American Mathematical Society