Title: | Oka domains in Euclidean spaces |
---|
Authors: | ID Forstnerič, Franc (Author) ID Wold, Erlend Fornæss (Author) |
Files: | URL - Source URL, visit https://academic.oup.com/imrn/article/2024/3/1801/7046029
PDF - Presentation file, download (278,96 KB) MD5: 9584BE27082D1363DAC666D0801A4741
|
---|
Language: | English |
---|
Typology: | 1.01 - Original Scientific Article |
---|
Organization: | IMFM - Institute of Mathematics, Physics, and Mechanics
|
---|
Abstract: | 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. |
---|
Keywords: | Oka manifold, hyperbolic manifolds, density property, projectively convex sets |
---|
Publication status: | Published |
---|
Publication version: | Version of Record |
---|
Publication date: | 01.02.2024 |
---|
Year of publishing: | 2024 |
---|
Number of pages: | str. 1801-1824 |
---|
Numbering: | Vol. 2024, iss. 3 |
---|
PID: | 20.500.12556/DiRROS-18209 |
---|
UDC: | 517.5 |
---|
ISSN on article: | 1687-0247 |
---|
DOI: | 10.1093/imrn/rnac347 |
---|
COBISS.SI-ID: | 143307011 |
---|
Note: |
|
---|
Publication date in DiRROS: | 19.02.2024 |
---|
Views: | 219 |
---|
Downloads: | 73 |
---|
Metadata: | |
---|
:
|
Copy citation |
---|
| | | Share: | |
---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |