Open Access
2019 An Interpolation Property of Locally Stein Sets
Viorel Vâjâitu
Publ. Mat. 63(2): 715-725 (2019). DOI: 10.5565/PUBLMAT6321909


We prove that, if $D $ is a normal open subset of a Stein space $X$ of pure dimension such that $D$ is locally Stein at every point of $\partial D \setminus X_{\operatorname{sg}}$, then, for every holomorphic vector bundle $E$ over $D$ and every discrete subset $\Lambda $ of $D \setminus X_{\operatorname{sg}}$ whose set of accumulation points lies in $\partial D \setminus X_{\operatorname{sg}}$, there is a holomorphic section of $E$ over $D$ with prescribed values on $\Lambda$. We apply this to the local Steinness problem and domains of holomorphy.


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Viorel Vâjâitu. "An Interpolation Property of Locally Stein Sets." Publ. Mat. 63 (2) 715 - 725, 2019.


Received: 27 November 2017; Revised: 3 September 2018; Published: 2019
First available in Project Euclid: 28 June 2019

zbMATH: 07094867
MathSciNet: MR3980938
Digital Object Identifier: 10.5565/PUBLMAT6321909

Primary: 32F10

Keywords: $\overline \partial$-problem , domain of holomorphy , Stein space

Rights: Copyright © 2019 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.63 • No. 2 • 2019
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