http://dx.doi.org/10.4153/CMB-2011-099-9
Canad. Math. Bull. 55(2012), 509-522
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.
© Canadian Mathematical Society, 2013
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