Analyse et géométrie complexes
Levi Problem: Complement of a closed subspace in a Stein space and its applications
Comptes Rendus. Mathématique, Tome 359 (2021) no. 8, pp. 1023-1046.

Let $Y$ be an open subset of a Stein space $X$. We show that if $Y$ is locally Stein and the complement $X-Y$ is a closed subspace of $X$, then $Y$ is Stein. We also discuss the applications of the theorem to open subsets $Y$ whose boundaries in $X$ are not closed subspaces of $X$. For example, we show that if for every boundary point $P\in \partial Y$, there is a closed subspace $H$ of pure codimension 1 in $X$ such that $P\in H$, $H\cap Y=\varnothing$ and $X-H$ is locally Stein, then $Y$ is Stein.

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DOI : https://doi.org/10.5802/crmath.244
Classification : 32E10,  32E40,  14C20
Jing Zhang 1

1. 1 University Parkway, Department of Mathematics, Division of Science, Mathematics and Technology, College of Arts and Sciences, Governors State University, University Park, IL 60484 USA.
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Jing Zhang. Levi Problem: Complement of a closed subspace in a Stein space and its applications. Comptes Rendus. Mathématique, Tome 359 (2021) no. 8, pp. 1023-1046. doi : 10.5802/crmath.244. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.244/

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