Title: | The Calabi-Yau problem for minimal surfaces with Cantor ends |
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Authors: | ID Forstnerič, Franc (Author) |
Files: | PDF - Presentation file, download (516,47 KB) MD5: 0BAFE7232DED29B49FB74D3E58B0F5E6
URL - Source URL, visit https://ems.press/journals/rmi/articles/6866102
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Language: | English |
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Typology: | 1.01 - Original Scientific Article |
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Organization: | IMFM - Institute of Mathematics, Physics, and Mechanics
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Abstract: | 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. |
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Keywords: | minimal surfaces, Calabi–Yau problem, null curve, Legendrian curve |
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Publication status: | Published |
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Publication version: | Version of Record |
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Publication date: | 01.01.2023 |
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Year of publishing: | 2023 |
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Number of pages: | str. 2067-2077 |
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Numbering: | Vol. 39, no. 6 |
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PID: | 20.500.12556/DiRROS-18630 ![Link is opened in a new window New window](teme/dirros/img/NovoOkno.png) |
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UDC: | 517.5 |
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ISSN on article: | 0213-2230 |
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DOI: | 10.4171/RMI/1365 ![Link is opened in a new window New window](teme/dirros/img/NovoOkno.png) |
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COBISS.SI-ID: | 176903939 ![Link is opened in a new window New window](teme/dirros/img/NovoOkno.png) |
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Note: |
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Publication date in DiRROS: | 08.04.2024 |
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Views: | 351 |
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Downloads: | 156 |
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Metadata: | ![Export as DC-RDF DC-RDF](teme/dirros/img/icon_dc_rdf.gif) |
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