On the mean curvature estimates for bounded submanifolds

Author:

Coghlan Leslie,Itokawa Yoe,Kosecki Roman

Abstract

A Liouville-type theorem is proved for strongly subharmonic functions on complete riemannian manifolds of bounded curvature. We use this to give a simple proof of a theorem of Jorge. Koutroufiotis and Xavier, which gives an estimate for the exterior size of a submanifold in terms of the sup of the length of its mean curvature.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference3 articles.

1. Chopping Riemannian manifolds;Cheeger, Jeff,1991

2. Isometric immersions into spheres;Hasanis, Thomas;J. Math. Soc. Japan,1981

3. An inequality between the exterior diameter and the mean curvature of bounded immersions;Jorge, Luquésio P. de M.;Math. Z.,1981

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Generalizations of the Liouville theorem;Differential Geometry and its Applications;2008-06

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