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On Hyperbolicity of Domains with StrictlyPseudoconvex Ends

Published online by Cambridge University Press:  20 November 2018

Adam Harris
Affiliation:
Department of Mathematics and Statistics, School of Science and Technology, University of New England Armidale, NSW 2351, Australia e-mail: adamh@turing.une.edu.au
Martin Kolář
Affiliation:
Department of Mathematics and Statistics, Masaryk University, BrnoCzech Republic e-mail: mkolar@math.muni.cz
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2014

References

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