The Calabi-Yau problem for minimal surfaces with Cantor ends

Forstnerič, Franc (author)

We show that every connected compact or bordered Riemann surface contains a Cantor set whose complement admits a complete conformal minimal immersion in ${\mathbb R}^3$ with bounded image. The analogous result holds for holomorphic immersions into any complex manifold of dimension at least ▫$2$▫, for holomorphic null immersions into ${\mathbb C}^n$ with $n \ge 3$, for holomorphic Legendrian immersions into an arbitrary complex contact manifold, and for superminimal immersions into any selfdual or anti-self-dual Einstein four-manifold.

• Language: English
• Keywords: minimal surfaces, Calabi–Yau problem, null curve, Legendrian curve
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.01.2023
• Year: 2023
• Number of pages: Str. 2067-2077
• Numbering: Vol. 39, no. 6
• PID: 20.500.12556/RUL-155603
• UDC: 517.5
• ISSN on article: 0213-2230
• DOI: 10.4171/RMI/1365
• COBISS.SI-ID: 176903939
• Publication date in RUL: 08.04.2024

Record is a part of a journal

• Title: Revista matemática iberoamericana
• Shortened title: Rev. mat. iberoam.
• Publisher: Consejo Superior de Investigaciones Científicas, Real Sociedad Matemática Española, Antonio Córdoba
• ISSN: 0213-2230
• COBISS.SI-ID: 26288128

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: minimalne ploskve, problem Calabi–Yau, ničelna krivulja, Legendrove krivulje