Geodesic
On defining functions and cores for unbounded domains.~III
Sbornik. Mathematics, Tome 212 (2021) no. 6, pp. 859-885

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We extend the authors' results on existence of global defining functions to a number of different settings. In particular, we relax the assumption on strict pseudoconvexity of the domain to strict $q$-pseudoconvexity and we consider more general situations, where the ambient space is an almost complex manifold or a complex space. We also investigate to what extent the assumption on smoothness of the boundary of the domains under consideration is necessary in our results. Bibliography: 27 titles.
Keywords: strictly pseudoconvex domains, plurisubharmonic defining functions
Mots-clés : core of a domain. 
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     title = {On defining functions and cores for unbounded {domains.~III}},
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T. Harz; N. Shcherbina; G. Tomassini. On defining functions and cores for unbounded domains.~III. Sbornik. Mathematics, Tome 212 (2021) no. 6, pp. 859-885. http://geodesic.mathdoc.fr/item/SM_2021_212_6_a4/