A note on the Nebenh\"ulle of Smooth Complete Hartogs Domains
Yunus E. Zeytuncu
TL;DR
This paper proves that smooth bounded pseudoconvex complete Hartogs domains in complex two-space have trivial Nebenhülle, utilizing smoothness to apply a theorem by D. Catlin.
Contribution
It establishes the triviality of Nebenhülle for a class of smooth pseudoconvex Hartogs domains, connecting geometric properties with existing theorems.
Findings
Smooth bounded pseudoconvex complete Hartogs domains have trivial Nebenhülle
Smoothness is essential for applying Catlin's theorem
The result links domain geometry with complex analysis properties
Abstract
It is shown that a smooth bounded pseudoconvex complete Hartogs domain in has trivial Nebenh\"ulle. The smoothness assumption is used to invoke a theorem of D. Catlin.
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Taxonomy
TopicsGeometric and Algebraic Topology · Analytic and geometric function theory · Geometry and complex manifolds