Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-26T08:29:43.507Z Has data issue: false hasContentIssue false
  • English
  • Français

A Radó theorem for complex spaces

Part of: Analytic continuation Analytic spaces Genetics and population dynamics

Published online by Cambridge University Press:  17 June 2021

Viorel Vîjîitu
Viorel Vîjîitu*
Affiliation:
Université de Lille, U.F.R. de Mathématiques, F-59655 Villeneuve d’Ascq Cedex, France
*
e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We generalize Radó’s extension theorem from the complex plane to reduced complex spaces.

Keywords

Radó’s theoremcomplex spacec-holomorphic function

MSC classification

Primary: 32D15: Continuation of analytic objects
Secondary: 32D20: Removable singularities 32C15: Complex spaces
Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 2 , June 2022 , pp. 466 - 472
Check for updates
Copyright
© Canadian Mathematical Society 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aupetit, B., Une généralisation du théorème d’extension de Radó . Manuscripta Math. 23(1977/78), 319–323.CrossRefGoogle Scholar
Behnke, H. and Stein, K., Modifikation komplexer Mannigfaltigkeiten und Riemannscher Gebiete . Math. Ann. 124(1951), 1–16.CrossRefGoogle Scholar
Cartan, H., Sur une extension d’un théorème de Radó . Math. Ann. 125(1952), 49–50.CrossRefGoogle Scholar
Chirka, E. M., Complex analytic sets, Kluwer Academic Publishers Group, Dordrecht, 1989.CrossRefGoogle Scholar
Forster, O., Zur Theorie der Steinschen Algebren und Moduln . Math. Z. 97(1967), 376–405.CrossRefGoogle Scholar
Heinz, E., Ein elementarer Beweis des Satzes von Radó–Behnke–Stein–Cartan über analytische Funktionen . Math. Ann. 131(1956), 258–259.CrossRefGoogle Scholar
Kaufman, R., A theorem of Radó . Math. Ann. 169(1967), 282.CrossRefGoogle Scholar
Kaup, L. and Kaup, B., Holomorphic functions of several variables, de Gruyter Studies in Mathematics, 3, De Gruyter, Berlin, 1983.CrossRefGoogle Scholar
Nagata, M., Local rings, Interscience, New York, 1962.Google Scholar
Radó, T., Über eine nicht fortsetzbare Riemannsche Mannigfaltigkeit . Math. Z. 20(1924), 1–6.CrossRefGoogle Scholar
Riihentaus, J., A note concerning Radó’s theorem . Math. Z. 182(1983), 159–165.CrossRefGoogle Scholar
Siu, Y. T., O N-approximable and holomorphic functions on complex spaces . Duke Math. J. 36(1969), 451–454.CrossRefGoogle Scholar
Spallek, K., Differenzierbare und holomorphe Funktionen auf analytischen Mengen . Math. Ann. 161(1965), 143–162.CrossRefGoogle Scholar
Stout, E. L., A generalization of a theorem of Radó . Math. Ann. 177(1968), 339–340.CrossRefGoogle Scholar
Whitney, H., Complex analytic varieties, Addison, Wesley, 1972.Google Scholar