Acta mathematica scientia, Series B >
A NOTE ON COMPLETE MANIFOLDS WITH FINITE VOLUME
Received date: 2013-05-09
Revised date: 2013-09-02
Online published: 2014-05-20
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
DENG Hong-Cun . A NOTE ON COMPLETE MANIFOLDS WITH FINITE VOLUME[J]. Acta mathematica scientia, Series B, 2014 , 34(3) : 807 -813 . DOI: 10.1016/S0252-9602(14)60051-5
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