On Hyperbolicity of Domains with Strictly Pseudoconvex Ends. (20th February 2014) - Harris, Adam; Kolář, Martin
Abstract: This article establishes a sufficient condition for Kobayashi hyperbolicity of unbounded domains in terms of curvature. Specifically, when $Ω \, \subset \, {{\mathbb{C}}^{n}}$ corresponds to a sub-level set of a smooth, real-valued function Ψ such that the form $ω \, =\, i\partial \bar{\partial }Ψ $ is Kähler and has bounded curvature outside a bounded subset, then this domain admits a hermitian metric of strictly negative holomorphic sectional curvature.