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
Full-text PDF Free Access
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.
-  Jeff Cheeger and Mikhael Gromov, Chopping Riemannian manifolds, Differential geometry, Pitman Monogr. Surveys Pure Appl. Math., vol. 52, Longman Sci. Tech., Harlow, 1991, pp. 85–94. MR 1173034
Hasanis, Isometric immersions into spheres, J. Math. Soc.
Japan 33 (1981), no. 3, 551–555. MR
L. Jorge and D. Koutroufiotis, An estimate for the curvature of bounded submanifolds, Amer. J. Math. 103 (1981), no. 4, 711–725. MR 623135, https://doi.org/10.2307/2374048
-  Luquésio P. de M. Jorge and Frederico V. Xavier, An inequality between the exterior diameter and the mean curvature of bounded immersions, Math. Z. 178 (1981), no. 1, 77–82. MR 627095, https://doi.org/10.1007/BF01218372
- J. Cheeger and M. Gromov, Chopping riemannian manifolds, preprint. MR 1173034 (93k:53034)
- L. Jorge and D. Koutroufiotis, An estimate for the curvature of bounded submanifolds, Amer. J. Math. 103 (1981), 711-725. MR 623135 (83d:53041b)
- 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)