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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the mean curvature estimates for bounded submanifolds


Authors: Leslie Coghlan, Yoe Itokawa and Roman Kosecki
Journal: Proc. Amer. Math. Soc. 114 (1992), 1173-1174
MSC: Primary 53C20; Secondary 53C42
DOI: https://doi.org/10.1090/S0002-9939-1992-1062829-4
MathSciNet review: 1062829
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1062829-4
Article copyright: © Copyright 1992 American Mathematical Society