| Naslov: | Oka domains in Euclidean spaces |
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| Avtorji: | ID Forstnerič, Franc (Avtor)
ID Wold, Erlend Fornæss (Avtor) |
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| Datoteke: |  URL - Izvorni URL, za dostop obiščite https://academic.oup.com/imrn/article/2024/3/1801/7046029
 PDF - Predstavitvena datoteka, prenos (278,96 KB)
MD5: 9584BE27082D1363DAC666D0801A4741
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| Jezik: | Angleški jezik |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
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| Povzetek: | In this paper, we find surprisingly small Oka domains in Euclidean spaces $\mathbb C^n$ of dimension $n>1$ at the very limit of what is possible. Under a mild geometric assumption on a closed unbounded convex set $E$ in $\mathbb C^n$, we show that $\mathbb C^n\setminus E$ is an Oka domain. In particular, there are Oka domains only slightly bigger than a halfspace, the latter being neither Oka nor hyperbolic. This gives smooth families of real hypersurfaces $\Sigma_t \subset \mathbb C^n$ for $t \in \mathbb R$ dividing $\mathbb C^n$ in an unbounded hyperbolic domain and an Oka domain such that at $t=0$, $\Sigma_0$ is a hyperplane and the character of the two sides gets reversed. More generally, we show that if $E$ is a closed set in $\mathbb C^n$ for $n>1$ whose projective closure $\overline E \subset \mathbb{CP}^n$ avoids a hyperplane $\Lambda \subset \mathbb{CP}^n$ and is polynomially convex in $\mathbb{CP}^n\setminus \Lambda\cong\mathbb C^n$, then $\mathbb C^n\setminus E$ is an Oka domain. |
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| Ključne besede: | Oka manifold, hyperbolic manifolds, density property, projectively convex sets |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 01.02.2024 |
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| Leto izida: | 2024 |
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| Št. strani: | str. 1801-1824 |
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| Številčenje: | Vol. 2024, iss. 3 |
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| PID: | 20.500.12556/DiRROS-18209  |
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| UDK: | 517.5 |
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| ISSN pri članku: | 1687-0247 |
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| DOI: | 10.1093/imrn/rnac347 |
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| COBISS.SI-ID: | 143307011 |
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| Opomba: |
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| Datum objave v DiRROS: | 19.02.2024 |
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| Število ogledov: | 189 |
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| Število prenosov: | 65 |
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| Metapodatki: |     |
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