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On the mean curvature estimates for bounded submanifolds

1992
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Proceedings of the American Mathematical Society
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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. We give a short proof of the following theorem of Jorge and Xavier [3]. Theorem 1. Let M and M be riemannian manifolds and let f ' : M -> M be an isometric immersion.

doi:10.1090/s0002-9939-1992-1062829-4
fatcat:vcnzeh7cpfeajj7di3c2m6zecq