On defining functions and cores for unbounded domains. III

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Abstract

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.

About the authors

Tobias Harz

University of Wuppertal

Email: harz@math.uni-wuppertal.de

Nikolai Vasil'evich Shcherbina

University of Wuppertal

Email: shcherbina@math.uni-wuppertal.de

Giuseppe Tomassini

Scuola Normale Superiore

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