Oka domains in Euclidean spaces

Forstnerič, Franc (avtor), Wold, Erlend Fornæss (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: Oka manifold, hyperbolic manifolds, density property, projectively convex sets
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2024
• Št. strani: Str. 1801-1824
• Številčenje: Vol. 2024, no. 3
• PID: 20.500.12556/RUL-154512
• UDK: 517.5
• ISSN pri članku: 1687-0247
• DOI: 10.1093/imrn/rnac347
• COBISS.SI-ID: 143307011
• Datum objave v RUL: 19.02.2024

FORSTNERIČ, Franc in WOLD, Erlend Fornæss, 2024, Oka domains in Euclidean spaces. International mathematics research notices [na spletu]. 2024. Vol. 2024, no. 3, p. 1801–1824. [Dostopano 18 april 2025]. DOI 10.1093/imrn/rnac347. Pridobljeno s: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=slv&id=154512

Gradivo je del revije

• Naslov: International mathematics research notices
• Skrajšan naslov: Int. math. res. not.
• Založnik: Oxford University Press
• ISSN: 1687-0247
• COBISS.SI-ID: 515379993

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: mnogoterost Oka, hiperbolične mnogoterosti, lastnost gostote, projektivno konveksna množica