On Hyperbolicity of Domains with Strictly Pseudoconvex Ends. (20th February 2014)

• Record Type: Journal Article
• Authors: Harris, Adam; Kolář, Martin
• Is Part Of: Canadian journal of mathematics. Volume 66:Number 1(2014)
• Page Start: 197
• Page End: 204
• Publication Date: 2014-02-20
• Subjects: 32Q45 -- 32Q35; Kobayashi hyperbolicity -- Kahler metric -- plurisubharmonic function; Mathematics -- Periodicals; Mathematics; Electronic journals; Periodicals; 510
• DOI: 10.4153/CJM-2012-036-4
• Languages: English
• ISSNs: 0008-414X

Abstract

Abstract: 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.