A Gap theorem for ends of complete manifolds

MingLiang Cai, Tobias Holck Colding, Dagang Yang

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Let (Mn, o) be a pointed open complete manifold with Ricci curvature bounded from below by 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 Aa and the dimension 71 of the manifold M". We will give a gap theorem in this paper which shows that there exists an such that M" has at most two ends We also give examples to show that, in dimension n > 4, such manifolds in general do not carry any complete metric with nonnegative Ricci Curvature for any.

Original languageEnglish (US)
Pages (from-to)247-250
Number of pages4
JournalProceedings of the American Mathematical Society
Volume123
Issue number1
DOIs
StatePublished - Jan 1 1995

Fingerprint

Ricci Curvature
Theorem
Nonnegative Curvature
4-manifold
Ball
Non-negative
Upper bound
Metric

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

A Gap theorem for ends of complete manifolds. / Cai, MingLiang; Colding, Tobias Holck; Yang, Dagang.

In: Proceedings of the American Mathematical Society, Vol. 123, No. 1, 01.01.1995, p. 247-250.

Research output: Contribution to journalArticle

Cai, MingLiang ; Colding, Tobias Holck ; Yang, Dagang. / A Gap theorem for ends of complete manifolds. In: Proceedings of the American Mathematical Society. 1995 ; Vol. 123, No. 1. pp. 247-250.
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