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Comptes Rendus. Mathématique
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 PY, there is a closed subspace H of pure codimension 1 in X such that PH, HY= 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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     title = {Levi {Problem:} {Complement} of a closed subspace in a {Stein} space and its applications},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1023--1046},
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     year = {2021},
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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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