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 [en]
Envelopes of holomorphy, truncated tube domains, holomorphic extension, Bochner tube, manifold, schlichtness
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-50074ISBN: 978-91-89786-44-8 (print)OAI: oai:DiVA.org:miun-50074DiVA, id: diva2:1818274
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At the time of the presentation of the thesis the following papers were unpublished: paper 1 and 2 (submitted).
2023-12-122023-12-092023-12-12Bibliographically approved
List of papers