### Abstract

Let (M^{n}, 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 language | English (US) |
---|---|

Pages (from-to) | 247-250 |

Number of pages | 4 |

Journal | Proceedings of the American Mathematical Society |

Volume | 123 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1995 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*123*(1), 247-250. https://doi.org/10.1090/S0002-9939-1995-1213856-8

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

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 123, no. 1, pp. 247-250. https://doi.org/10.1090/S0002-9939-1995-1213856-8

}

TY - JOUR

T1 - A Gap theorem for ends of complete manifolds

AU - Cai, MingLiang

AU - Colding, Tobias Holck

AU - Yang, Dagang

PY - 1995/1/1

Y1 - 1995/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84966232789&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966232789&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1995-1213856-8

DO - 10.1090/S0002-9939-1995-1213856-8

M3 - Article

AN - SCOPUS:84966232789

VL - 123

SP - 247

EP - 250

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -