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Domains of Injective Holomorphy
Published online by Cambridge University Press: 20 November 2018
Abstract
A domain $\Omega $ is called a domain of injective holomorphy if there exists an injective holomorphic function $f\,:\,\Omega \,\to \,\mathbb{C}$ 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 $(\overset{\multimap }{\mathop{\Omega }}\,\,=\,\Omega )$ is a domain of injective holomorphy, and every simply connected domain is a domain of injective holomorphy as well.
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- Copyright © Canadian Mathematical Society 2012