On the characterization of parabolicity and hyperbolicity of submanifolds

On the characterization of parabolicity and hyperbolicity of submanifolds

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.

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Veröffentlicht in:Journal of the London Mathematical Society 2011-08, Vol.84 (1), p.120-136
Hauptverfasser: Esteve, Antonio, Palmer, Vicente
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0024-6107
1469-7750
DOI:10.1112/jlms/jdr001