Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A gap theorem for ends of complete manifolds
HTML articles powered by AMS MathViewer

by Mingliang Cai, Tobias Holck Colding and DaGang Yang PDF
Proc. Amer. Math. Soc. 123 (1995), 247-250 Request permission

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
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
  • © Copyright 1995 American Mathematical Society
  • 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