Geodesic
Domains of Injective Holomorphy
Canadian mathematical bulletin, Tome 55 (2012) no. 3, pp. 509-522

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DOI

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.
DOI : 10.4153/CMB-2011-099-9
Mots-clés : 30Exx, domains of holomorphy 
Gauthier, P. M.; Nestoridis, V. Domains of Injective Holomorphy. Canadian mathematical bulletin, Tome 55 (2012) no. 3, pp. 509-522. doi: 10.4153/CMB-2011-099-9
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     title = {Domains of {Injective} {Holomorphy}},
     journal = {Canadian mathematical bulletin},
     pages = {509--522},
     year = {2012},
     volume = {55},
     number = {3},
     doi = {10.4153/CMB-2011-099-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-099-9/}
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