Counting ends on complete smooth metric measure spaces

Wu, Jia-Yong

doi:10.1090/proc/12982

Counting ends on complete smooth metric measure spaces
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Proc. Amer. Math. Soc. 144 (2016), 2231-2239 Request permission

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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