| Title: | The Calabi-Yau problem for minimal surfaces with Cantor ends |
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| Authors: | ID Forstnerič, Franc (Author) |
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| 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  |
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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 |
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| COBISS.SI-ID: | 176903939 |
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| Note: |
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| Publication date in DiRROS: | 08.04.2024 |
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| Views: | 453 |
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| Downloads: | 198 |
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| Metadata: |    |
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