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1. CJM 2012 (vol 66 pp. 197)

Harris, Adam; Kolář, Martin
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 $\Psi$, such that the form $\omega = {\bf i}\partial\bar{\partial}\Psi$ is Kähler and has bounded curvature outside a bounded subset, then this domain admits a hermitian metric of strictly negative holomorphic sectional curvature.

Keywords:Kobayashi-hyperbolicity, Kähler metric, plurisubharmonic function
Categories:32Q45, 32Q35

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