| Title: | Proper holomorphic maps in Euclidean spaces avoiding unbounded convex sets |
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| Authors: | ID Drinovec-Drnovšek, Barbara (Author)
ID Forstnerič, Franc (Author) |
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| Files: |  URL - Source URL, visit https://link.springer.com/article/10.1007/s12220-023-01222-z
 PDF - Presentation file, download (441,34 KB)
MD5: 255FCE81E4C9F637CDC77BA233B7BBD4
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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 if $E$ is a closed convex set in $\mathbb C^n$, $n>1$ contained in a closed halfspace $H$ such that ▫$E\cap bH$▫ is nonempty and bounded, then the concave domain $\Omega=\mathbb C^n\setminus E$ contains images of proper holomorphicmaps $f : X \to \mathbb C^n$ from any Stein manifold $X$ of dimension $< n$, with approximation of a givenmap on closed compact subsets of $X$. If in addition $2 {\rm dim} X+1 \le n$ then $f$ can be chosen an embedding, and if $2 {\rm dim} X = n$, then it can be chosen an immersion. Under a stronger condition on $E$, we also obtain the interpolation property for such maps on closed complex subvarieties. |
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| Keywords: | Stein manifolds, holomorphic embeddings, Oka manifold, minimal surfaces, convexity |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.06.2023 |
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| Year of publishing: | 2023 |
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| Number of pages: | art. 170 (22 str.) |
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| Numbering: | Vol. 33, iss. 6 |
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| PID: | 20.500.12556/DiRROS-18406  |
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| UDC: | 517.5 |
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| ISSN on article: | 1050-6926 |
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| DOI: | 10.1007/s12220-023-01222-z |
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| COBISS.SI-ID: | 147026947 |
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| Note: | Spletna objava: 28. 3. 2023;
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| Publication date in DiRROS: | 15.03.2024 |
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| Views: | 949 |
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| Downloads: | 557 |
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