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# Domains of Injective Holomorphy

Published:2011-05-20
Printed: Sep 2012
• P. M. Gauthier,
Département de Mathématiques et statistiques, Université de Montréal, Montreal, QC H3C 3J7
• V. Nestoridis,
Department of Mathematics, University of Athens, Panepistimioupolis GR-157 84, Athens, Greece
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## Abstract

A domain $\Omega$ is called a domain of injective holomorphy if there exists an injective holomorphic function $f\colon \Omega\rightarrow\mathbb{C}$ that is non-extendable. We give examples of domains that are domains of injective holomorphy and others that are not. In particular, every regular domain $(\overline\Omega^o=\Omega)$ is a domain of injective holomorphy, and every simply connected domain is a domain of injective holomorphy as well.
 Keywords: domains of holomorphy domains of holomorphy
 MSC Classifications: 30Exx - Miscellaneous topics of analysis in the complex domain