The nonhomogeneous Cauchy-Riemann equation on families of open Riemann surfaces

Forstnerič, Franc (author)

In this paper, we use the nonhomogeneous Beltrami equation to give an optimal solution to the nonhomogeneous Cauchy-Riemann equation for continuous or smooth families of complex structures and $(0, 1)$-forms of a Hölder class on a smooth open orientable surface. As an application, we obtain the Oka-Grauert principle for complex line bundles on families of open Riemann surfaces.

• Language: English
• Keywords: Riemann surfaces, Cauchy-Riemann equation, Oka-Grauert principle, Oka manifold
• 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: 2026
• Number of pages: 7 str.
• Numbering: Vol. 12, iss. 1, art. 7
• PID: 20.500.12556/RUL-177638
• UDC: 517.5
• ISSN on article: 2197-120X
• DOI: 10.1007/s40627-025-00189-7
• COBISS.SI-ID: 263139843
• Publication date in RUL: 30.12.2025

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: Riemannove ploskve, Cauchy-Riemannova enačba, princip Oka-Grauert, mnogoterost Oka