Hartogs-type Extension for Tube-like Domains in C²

Author

Al Boggess
Roman Dwilewicz, Missouri University of Science and TechnologyFollow
Zbigniew Slodkowski

Abstract

In this paper we consider the Hartogs-type extension problem for unbounded domains in C². An easy necessary condition for a domain to be of Hartogs-type is that there is not a closed (in C²) complex variety of codimension one in the domain which is given by a holomorphic function smooth up to the boundary. The question is, how far this necessary condition is from the sufficient one? To show how complicated this question is, we give a class of tube-like domains which contain a complex line in the boundary which are either of Hartogs-type or not, depending on how the complex line is positioned with respect to the domain.

Recommended Citation

A. Boggess et al., "Hartogs-type Extension for Tube-like Domains in C²," Mathematische Annalen, vol. 363, no. 1 thru 2, pp. 35 - 60, Springer, Oct 2015.

The definitive version is available at https://doi.org/10.1007/s00208-014-1161-0

Department(s)

Mathematics and Statistics

Publication Status

Full / Open Access

Keywords and Phrases

32D15; Primary 32V10; Secondary 32V25

International Standard Serial Number (ISSN)

0025-5831

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2024 Springer, All rights reserved.

Publication Date

13 Oct 2015