Acta mathematica scientia, Series B >
AN ESTIMATE FOR THE MEAN CURVATURE OF SUBMANIFOLDS CONTAINED IN A HOROBALL
Received date: 2012-07-31
Online published: 2013-11-20
Supported by
The research is partially supported by the National Natural Science Foundation of China (11126189, 11171259), Specialized Research Fund for the Doctoral Program of Higher Education (20120141120058), China Postdoctoral Science Foundation Funded Project (20110491212) and the Fundamental Research Funds for the Central Universities (2042011111054).
We obtain the Omori-Yau maximum principle on complete properly immersed submanifolds with the mean curvature satisfying certain condition in complete Riemannian manifolds whose radial sectional curvature satisfies some decay condition, which generalizes our previous results in [17]. Using this generalized maximum principle, we give an estimate
on the mean curvature of properly immersed submanifolds in Hn ×R? with the image under the projection on Hn contained in a horoball and the corresponding situation in hyperbolic space. We also give other applications of the generalized maximum principle.
Key words： Omori-Yau maximum principle; proper; mean curvature; horoball; hyper-bolic space
QIU Hong-Bing . AN ESTIMATE FOR THE MEAN CURVATURE OF SUBMANIFOLDS CONTAINED IN A HOROBALL[J]. Acta mathematica scientia, Series B, 2013 , 33(6) : 1561 -1570 . DOI: 10.1016/S0252-9602(13)60104-6
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