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Truncated tube domains with multi-sheeted envelope
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Mathematics, and Science Education (2023-).ORCID iD: 0000-0001-6715-7852
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Mathematics, and Science Education (2023-).
(English)In: Article in journal (Other academic) Submitted
Abstract [en]

The present article is concerned with a group of problems raised by J. Noguchi and M. Jarnicki/P. Plug, namely whether the envelopes of holomorphy of truncated tube domains are always schlicht, i.e. subdomains of $\mathbb{C}^n$, and how to characterize 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 envelopes have arbitrarily many sheets. The article is concluded by sufficient conditions for schlichtness in complex dimension two.

National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-50071OAI: oai:DiVA.org:miun-50071DiVA, id: diva2:1818272
Note

Preprintversion i Arxiv, doi: https://doi.org/10.48550/arXiv.2306.00441 

Available from: 2023-12-09 Created: 2023-12-09 Last updated: 2024-09-26
In thesis
1. Holomorphic extension and schlichtness on tube manifolds
Open this publication in new window or tab >>Holomorphic extension and schlichtness on tube manifolds
2023 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

We first investigate the holomorphic extension of some classical and accessible classes of domains in $\mathbb{C}^n$ to know to what extent their envelopes are constructive. We give alternative proofs to some of the classical theorems using only first-principle arguments and without involving higher Stein geometry. Next, we address an open problem asked by M. Jarnicki/P. Pflug and construct a counter-example to provide a negative answer to a related open question asked by J. Noguchi, which asks whether the envelopes of holomorphy of truncated tube domains are always schlicht. We also provide a sufficient condition for schlichtness of a tube domain $X+iY$ in $\mathbb{C}^2$, for which $X\subset \mathbb{R}^2$ is a convex domain consisting of finitely many holes with strictly convex $\mathcal{C}^2$-boundary, and $Y\subset \mathbb{R}^2$ is a convex domain.

Place, publisher, year, edition, pages
Sundsvall: Mid Sweden University, 2023. p. 40
Series
Mid Sweden University licentiate thesis, ISSN 1652-8948 ; 199
Keywords
Envelopes of holomorphy, truncated tube domains, holomorphic extension, Bochner tube, manifold, schlichtness
National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-50074 (URN)978-91-89786-44-8 (ISBN)
Presentation
2023-12-15, C312, Holmgatan 10, Sundsvall, 13:00 (English)
Opponent
Supervisors
Note

Vid tidpunkten för presentationen av avhandlingen var följande delarbeten opublicerade: delarbete 1 och 2 (inskickade).

At the time of the presentation of the thesis the following papers were unpublished: paper 1 and 2 (submitted).

Available from: 2023-12-12 Created: 2023-12-09 Last updated: 2023-12-12Bibliographically approved

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Hazra, SuprokashPorten, Egmont

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CiteExportLink to record
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Citation style
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