数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (3): 807-813.doi: 10.1016/S0252-9602(14)60051-5

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A NOTE ON COMPLETE MANIFOLDS WITH FINITE VOLUME

邓洪存   

  1. Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
  • 收稿日期:2013-05-09 修回日期:2013-09-02 出版日期:2014-05-20 发布日期:2014-05-20

A NOTE ON COMPLETE MANIFOLDS WITH FINITE VOLUME

DENG Hong-Cun   

  1. Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
  • Received:2013-05-09 Revised:2013-09-02 Online:2014-05-20 Published:2014-05-20

摘要:

In this article, we concern on complete manifolds with finite volume. We prove that under some assumptions about scalar curvature and the Yamabe constant, the manifolds must be compact, and we also give the diameter estimates in terms of the scalar curvature and the Yamabe constant.

关键词: Diameter, scalar curvature, complete manifold with finite volume

Abstract:

In this article, we concern on complete manifolds with finite volume. We prove that under some assumptions about scalar curvature and the Yamabe constant, the manifolds must be compact, and we also give the diameter estimates in terms of the scalar curvature and the Yamabe constant.

Key words: Diameter, scalar curvature, complete manifold with finite volume

中图分类号: 

  • 53C21