Counting ends on complete smooth metric measure spaces
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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.References
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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
- Received by editor(s): June 17, 2015
- Published electronically: December 15, 2015
- Communicated by: Guofang Wei
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 2231-2239
- MSC (2010): Primary 53C20
- DOI: https://doi.org/10.1090/proc/12982
- MathSciNet review: 3460181