AN ESTIMATE FOR THE SECTIONAL CURVATURE OF CYLINDRICALLY BOUNDED SUBMANIFOLDS

作者：Alias Luis J^*; Pacelli Bessa G; Fabio Montenegro J

来源：Transactions of the American Mathematical Society, 2012, 364(7): 3513-3528.

DOI：10.1090/S0002-9947-2012-05439-0

• Omori-Yau Maximum Principle
• cylindrically bounded submanifolds
• properly immersed submanifolds

We give sharp sectional curvature estimates for complete immersed cylindrically bounded m-submanifolds phi: M-m -%26gt; Nn-l x R-l, n + l %26lt;= 2m - 1, provided that either phi is proper with the norm of the second fundamental form with certain controlled growth or M has scalar curvature with strong quadratic decay. The latter gives a non-trivial extension of the Jorge-Koutrofiotis Theorem. In the particular case of hypersurfaces, that is, m = n - 1, the growth rate of the norm of the second fundamental form is improved. Our results will be an application of a generalized Omori-Yau Maximum Principle for the Hessian of a Riemannian manifold, in its newest elaboration given by Pigola, Rigoli and Setti (2005).

• 出版日期2012-7