On the characterization of parabolicity and hyperbolicity of submanifolds
arXiv:0909.0422 · doi:10.1112/jlms/jdr001
Abstract
We give a set of sufficient and necessary conditions for parabolicity and hyperbolicity of a submanifold with controlled mean curvature in a Riemannian manifold with a pole and with sectional curvatures bounded from above or from below.
19 pages