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October 2022 Stein neighbourhoods of bordered complex curves attached to holomorphically convex sets
F. Forstnerič
Author Affiliations +
Ark. Mat. 60(2): 335-349 (October 2022). DOI: 10.4310/ARKIV.2022.v60.n2.a6

Abstract

In this paper, we construct open Stein neighbourhoods of compact sets of the form $A \cup K$ in a complex space, where $K$ is a compact holomorphically convex set, $A$ is a compact complex curve with boundary $bA$ of class $\mathscr{C}^2$ which may intersect $K$, and the set $A \cap K$ is $\mathscr{O}(A)$-convex.

Funding Statement

The author’s research was supported in part by the research program P1-0291 and grants J1-9104 and J1-3005 from ARRS, Republic of Slovenia.

Citation

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F. Forstnerič. "Stein neighbourhoods of bordered complex curves attached to holomorphically convex sets." Ark. Mat. 60 (2) 335 - 349, October 2022. https://doi.org/10.4310/ARKIV.2022.v60.n2.a6

Information

Received: 20 April 2021; Accepted: 22 March 2022; Published: October 2022
First available in Project Euclid: 17 July 2024

Digital Object Identifier: 10.4310/ARKIV.2022.v60.n2.a6

Subjects:
Primary: 32E10 , 32E20 , 32U05

Keywords: complex curve , holomorphically convex set , Stein manifold

Rights: Copyright © 2022 Institut Mittag-Leffler

Vol.60 • No. 2 • October 2022
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