Truncated tube domains with multi-sheeted envelope

Hazra, Suprokash; Porten, Egmont

doi:10.1090/proc/17179

Truncated tube domains with multi-sheeted envelope
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by Suprokash Hazra and Egmont Porten;

Proc. Amer. Math. Soc.

DOI: https://doi.org/10.1090/proc/17179

Published electronically: April 30, 2025

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Abstract:

The present article is concerned with a group of problems raised by J. Noguchi and M. Jarnicki/P. Pflug, namely whether the envelopes of holomorphy of truncated tube domains are always schlicht, that is, subdomains of $\mathbb {C}^n$, and how to characterise schlichtness if this is not the case. By way of a counter-example homeomorphic to the $4$-ball, we answer the first question in the negative. Moreover, it is possible that the envelope has arbitrarily many sheets. The article is concluded by sufficient conditions for schlichtness in complex dimension two.

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Truncated tube domains with multi-sheeted envelope
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Abstract: