Comptes Rendus
Analyse et géométrie complexes
Levi Problem: Complement of a closed subspace in a Stein space and its applications
Comptes Rendus. Mathématique, Volume 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.

Reçu le :
Accepté le :
Publié le :
DOI : 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.
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Jing Zhang. Levi Problem: Complement of a closed subspace in a Stein space and its applications. Comptes Rendus. Mathématique, Volume 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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