A gap theorem for ends of complete manifolds

Authors:
Mingliang Cai, Tobias Holck Colding and DaGang Yang

Journal:
Proc. Amer. Math. Soc. **123** (1995), 247-250

MSC:
Primary 53C20; Secondary 53C21

DOI:
https://doi.org/10.1090/S0002-9939-1995-1213856-8

MathSciNet review:
1213856

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Abstract: Let be a pointed open complete manifold with Ricci curvature bounded from below by (for ) and nonnegative outside the ball . It has recently been shown that there is an upper bound for the number of ends of such a manifold which depends only on and the dimension *n* of the manifold . We will give a gap theorem in this paper which shows that there exists an such that has at most two ends if . We also give examples to show that, in dimension , such manifolds in general do not carry any complete metric with nonnegative Ricci Curvature for any .

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DOI:
https://doi.org/10.1090/S0002-9939-1995-1213856-8

Article copyright:
© Copyright 1995
American Mathematical Society