Geodesic
On Hyperbolicity of Domains with StrictlyPseudoconvex Ends
Canadian journal of mathematics, Tome 66 (2014) no. 1, pp. 197-204

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DOI

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.
DOI : 10.4153/CJM-2012-036-4
Mots-clés : 32Q45, 32Q35, Kobayashi hyperbolicity, Kahler metric, plurisubharmonic function 
Harris, Adam; Kolář, Martin. On Hyperbolicity of Domains with StrictlyPseudoconvex Ends. Canadian journal of mathematics, Tome 66 (2014) no. 1, pp. 197-204. doi: 10.4153/CJM-2012-036-4
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     title = {On {Hyperbolicity} of {Domains} with {StrictlyPseudoconvex} {Ends}},
     journal = {Canadian journal of mathematics},
     pages = {197--204},
     year = {2014},
     volume = {66},
     number = {1},
     doi = {10.4153/CJM-2012-036-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2012-036-4/}
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