Complex analysis and geometry
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.

Received:
Accepted:
Published online:
DOI: 10.5802/crmath.244
Classification: 32E10, 32E40, 14C20
Zhang, Jing 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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Zhang, Jing. 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. http://www.numdam.org/articles/10.5802/crmath.244/

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