Approximation of biholomorphic maps between Runge domains by holomorphic automorphisms

Forstnerič, Franc (author)

We show that biholomorphic maps between certain pairs of Runge domains in the complex affine space ${\mathbb C}^n$, $n > 1$, are limits of holomorphic automorphisms of ${\mathbb C}^n$. A similar result holds for volume preserving maps and also in Stein manifolds with the density property. This generalises several results in the literature with considerably simpler proofs.

• Language: English
• Keywords: Runge domains, holomorphic automorphisms, Stein manifolds, density property
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: 4 str.
• Numbering: Vol. 11, iss. 3, art. 13
• PID: 20.500.12556/RUL-175466
• UDC: 517.5
• ISSN on article: 2197-120X
• DOI: 10.1007/s40627-025-00163-3
• COBISS.SI-ID: 246516227
• Publication date in RUL: 28.10.2025

Record is a part of a journal

• Title: Complex analysis and its synergies
• Shortened title: Complex analysis synerg.
• Publisher: Springer, Springer Nature
• ISSN: 2197-120X
• COBISS.SI-ID: 525369113

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: Rungejeva domena, holomorfni avtomorfizmi, Steinove mnogoterosti, lastnost gostote