The mean curvature of cylindrically bounded submanifolds
| Autor: | Alias, L. J., Bessa, G. Pacelli, Dajczer, M. |
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| Rok vydání: | 2008 |
| Předmět: | |
| Zdroj: | Mathematische Annalen 345 (2009), 367--376. |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00208-009-0357-1 |
| Popis: | We give an estimate of the mean curvature of a complete submanifold lying inside a closed cylinder $B(r)\times\R^{\ell}$ in a product Riemannian manifold $N^{n-\ell}\times\R^{\ell}$. It follows that a complete hypersurface of given constant mean curvature lying inside a closed circular cylinder in Euclidean space cannot be proper if the circular base is of sufficiently small radius. In particular, any possible counterexample to a conjecture of Calabion complete minimal hypersurfaces cannot be proper. As another application of our method, we derive a result about the stochastic incompleteness of submanifolds with sufficiently small mean curvature. Comment: First version (December 2008). Final version, including new title (February 2009). To appear in Mathematische Annalen |
| Databáze: | arXiv |
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