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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
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.

References [Enhancements On Off] (What's this?)

  • [1] J. Cheeger and M. Gromov, Chopping riemannian manifolds, preprint. MR 1173034 (93k:53034)
  • [2] L. Jorge and D. Koutroufiotis, An estimate for the curvature of bounded submanifolds, Amer. J. Math. 103 (1981), 711-725. MR 623135 (83d:53041b)
  • [3] L. Jorge and F. Xavier, An inequality between the exterior diameter and the mean curvature of bounded immersions, Math. Z. 178 (1981), 77-82. MR 627095 (82k:53080)

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Article copyright: © Copyright 1992 American Mathematical Society

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