Levi Problem: Complement of a closed subspace in a Stein space and its applications

Jing Zhang

doi:10.5802/crmath.244

Analyse et géométrie complexes

Levi Problem: Complement of a closed subspace in a Stein space and its applications

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.

Comptes Rendus. Mathématique, Volume 359 (2021) no. 8, pp. 1023-1046.

Résumé

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 $P \in H$ , $H \cap Y = \emptyset$ and $X - H$ is locally Stein, then $Y$ is Stein.

Reçu le : 2019-11-11
Accepté le : 2021-07-13
Publié le : 2021-10-08

DOI : 10.5802/crmath.244

Classification : 32E10, 32E40, 14C20

Affiliations des auteurs :

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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     author = {Jing Zhang},
     title = {Levi {Problem:} {Complement} of a closed subspace in a {Stein} space and its applications},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1023--1046},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {8},
     year = {2021},
     doi = {10.5802/crmath.244},
     language = {en},
}

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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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