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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Convex domains and Kobayashi hyperbolicity


Author: Theodore J. Barth
Journal: Proc. Amer. Math. Soc. 79 (1980), 556-558
MSC: Primary 32H20; Secondary 32F15, 32F99
MathSciNet review: 572300
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Abstract: A geometrically convex domain in $ {{\mathbf{C}}^n}$ is Kobayashi hyperbolic if and only if it contains no complex affine lines. This contrasts with an example of a nonhyperbolic pseudoconvex domain in $ {{\mathbf{C}}^2}$ containing no (nonconstant) entire holomorphic curves.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0572300-3
PII: S 0002-9939(1980)0572300-3
Keywords: Carathéodory pseudodistance, Kobayashi pseudodistance, convex domain, pseudoconvex domain
Article copyright: © Copyright 1980 American Mathematical Society