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On Hyperbolicity of Domains with Strictly Pseudoconvex Ends
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- Journal:
- Canadian Journal of Mathematics / Volume 66 / Issue 1 / February 2014
- Published online by Cambridge University Press:
- 20 November 2018, pp. 197-204
- Print publication:
- February 2014
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- Article
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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.
