On Hyperbolicity of Domains with Strictly Pseudoconvex Ends

This article establishes a sufficient condition for Kobayashi hyperbolicity of unbounded domains in terms of curvature. Specifically, when $\Omega \,\subset \,{{\mathbb{C}}^{n}}$ corresponds to a sub-level set of a smooth, real-valued function Ψ such that the form $\omega \,=\,\mathbf{i}\partial \ba...

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Bibliographic Details
Published in:Canadian journal of mathematics 2014-02, Vol.66 (1), p.197-204
Main Authors: Harris, Adam, Kolář, Martin
Format: Article
Language:English
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Summary:This article establishes a sufficient condition for Kobayashi hyperbolicity of unbounded domains in terms of curvature. Specifically, when $\Omega \,\subset \,{{\mathbb{C}}^{n}}$ corresponds to a sub-level set of a smooth, real-valued function Ψ such that the form $\omega \,=\,\mathbf{i}\partial \bar{\partial }\Psi $ is Kähler and has bounded curvature outside a bounded subset, then this domain admits a hermitian metric of strictly negative holomorphic sectional curvature.
ISSN:0008-414X
1496-4279
DOI:10.4153/CJM-2012-036-4