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On Hyperbolicity of Domains with Strictly Pseudoconvex Ends

  Published:2012-12-04
 Printed: Feb 2014
  • Adam Harris,
    Department of Mathematics and Statistics, School of Science and Technology, University of New England Armidale, NSW 2351 Australia
  • Martin Kolář,
    Department of Mathematics and Statistics, Masaryk University, Janackovo nam. 2a, 662 95 Brno
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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 $\Psi$, 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 Kobayashi-hyperbolicity, Kähler metric, plurisubharmonic function
MSC Classifications: 32Q45, 32Q35 show english descriptions Hyperbolic and Kobayashi hyperbolic manifolds
Complex manifolds as subdomains of Euclidean space
32Q45 - Hyperbolic and Kobayashi hyperbolic manifolds
32Q35 - Complex manifolds as subdomains of Euclidean space
 

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