AN ESTIMATE FOR THE MEAN CURVATURE OF SUBMANIFOLDS CONTAINED IN A HOROBALL

doi:10.1016/S0252-9602(13)60104-6

Abstract

Abstract:

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

CLC Number:

53C40

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.

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