| Title: | Embedded complex curves in the affine plane |
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| Authors: | ID Alarcón, Antonio (Author)
ID Forstnerič, Franc (Author) |
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| Files: |  PDF - Presentation file, download (579,03 KB)
MD5: 66C25739058840A607CD00C8F60979C1
 URL - Source URL, visit https://link.springer.com/article/10.1007/s10231-023-01418-8
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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: | This paper brings several contributions to the classical Forster-Bell-Narasimhan conjecture and the Yang problem concerning the existence of proper and almost proper (hence complete) injective holomorphic immersions of open Riemann surfaces in the affine plane ${\mathbb C}^2$ satisfying interpolation and hitting conditions. We also show that in every compact Riemann surface there is a Cantor set whose complement admits a proper holomorphic embedding in ${\mathbb C}^2$. The focal point is a lemma saying the following. Given a compact bordered Riemann surface, $M$, a closed discrete subset $E$ of its interior ${\mathring M}=M\setminus bM$, a compact subset $K\subset {\mathring M}\setminus E$ without holes in $\mathring M$, and a ${\cal C}^1$ embedding $f: M\hookrightarrow \mathbb C^2$ which is holomorphic in $\mathring M$, we can approximate $f$ uniformly on $K$ by a holomorphic embedding $F: bM\hookrightarrow {\mathbb C}^2$ which maps $E\cup bM$ out of a given ball and satisfies some interpolation conditions. |
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| Keywords: | Riemann surfaces, complex curves, complete holomorphic embedding |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.08.2024 |
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| Year of publishing: | 2024 |
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| Number of pages: | str. 1673-1701 |
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| Numbering: | Vol. 203, iss. 4 |
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| PID: | 20.500.12556/DiRROS-19296  |
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| UDC: | 517.5 |
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| ISSN on article: | 0373-3114 |
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| DOI: | 10.1007/s10231-023-01418-8 |
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| COBISS.SI-ID: | 182950147 |
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| Note: |
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| Publication date in DiRROS: | 15.07.2024 |
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| Views: | 310 |
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| Downloads: | 170 |
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| Metadata: |    |
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