Flexible domains for minimal surfaces in Euclidean spaces

Drinovec-Drnovšek, Barbara (author), Forstnerič, Franc (author)

In this paper we introduce and investigate a new notion of flexibility for domains in Euclidean spaces $\mathbb{R}^n$ for $n\ge 3$ in terms of minimal surfaces which they contain. A domain $\Omega$ in $\mathbb{R}^n$ is said to be flexible if every conformal minimal immersion $U \to \Omega$ from a Runge domain $U$ in an open conformal surface $M$ can be approximated uniformly on compacts, with interpolation on any given finite set, by conformal minimal immersion $M \to \Omega$. Together with hyperbolicity phenomena considered in recent works, this extends the dichotomy between flexibility and rigidity from complex analysis to minimal surface theory.

• Language: English
• Keywords: minimal surface, flexible domain, hyperbolic domain, Oka manifold, keywords minimal surface
• 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: 2023
• Number of pages: 15 str.
• Numbering: Vol. 517, iss. 2, art. 126653
• PID: 20.500.12556/RUL-140155
• UDC: 517.55:514.7
• ISSN on article: 0022-247X
• DOI: 10.1016/j.jmaa.2022.126653
• COBISS.SI-ID: 120880899
• Publication date in RUL: 12.09.2022

Record is a part of a journal

• Title: Journal of mathematical analysis and applications
• Shortened title: J. math. anal. appl.
• Publisher: Elsevier
• ISSN: 0022-247X
• COBISS.SI-ID: 3081231

Licences

• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.

Secondary language

• Language: Slovenian
• Keywords: minimalna ploskev, fleksibilna domena, hiperbolična domena, Okova mnogoterost