Abstract view
|
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
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.
