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Counting ends on complete smooth metric measure spaces


Author: Jia-Yong Wu
Journal: Proc. Amer. Math. Soc. 144 (2016), 2231-2239
MSC (2010): Primary 53C20
DOI: https://doi.org/10.1090/proc/12982
Published electronically: December 15, 2015
MathSciNet review: 3460181
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ (M, g,e^{-f}dv)$ be a complete smooth metric measure space with Bakry-Émery Ricci curvature nonnegative outside a compact set. We prove that the number of ends of such a measure space is finite if $ f$ has at most sublinear growth outside the compact set. In particular, we give an explicit upper bound for the number.


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Additional Information

Jia-Yong Wu
Affiliation: Department of Mathematics, Shanghai Maritime University, 1550 Haigang Avenue, Shanghai 201306, People’s Republic of China
Email: jywu81@yahoo.com

DOI: https://doi.org/10.1090/proc/12982
Keywords: Smooth metric measure space, Bakry-\'Emery Ricci curvature, end.
Received by editor(s): June 17, 2015
Published electronically: December 15, 2015
Communicated by: Guofang Wei
Article copyright: © Copyright 2015 American Mathematical Society

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