Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



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
MathSciNet review: 1213856
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $({M^n},o)$ be a pointed open complete manifold with Ricci curvature bounded from below by $- (n - 1){\Lambda ^2}$ (for $\Lambda \geq 0$) and nonnegative outside the ball $B(o,a)$. It has recently been shown that there is an upper bound for the number of ends of such a manifold which depends only on $\Lambda a$ and the dimension n of the manifold ${M^n}$. We will give a gap theorem in this paper which shows that there exists an $\varepsilon = \varepsilon (n) > 0$ such that ${M^n}$ has at most two ends if $\Lambda a \leq \varepsilon (n)$. We also give examples to show that, in dimension $n \geq 4$, such manifolds in general do not carry any complete metric with nonnegative Ricci Curvature for any $\Lambda a > 0$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53C20, 53C21

Retrieve articles in all journals with MSC: 53C20, 53C21

Additional Information

Article copyright: © Copyright 1995 American Mathematical Society