| Title: | Proper holomorphic maps in Euclidean spaces avoiding unbounded convex sets |
|---|
| Authors: | ID Drinovec-Drnovšek, Barbara (Author)
ID Forstnerič, Franc (Author) |
|---|
| 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
|
|---|
| Language: | English |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
|
|---|
| 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. |
|---|
| Keywords: | Stein manifolds, holomorphic embeddings, Oka manifold, minimal surfaces, convexity |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Publication date: | 01.06.2023 |
|---|
| Year of publishing: | 2023 |
|---|
| Number of pages: | art. 170 (22 str.) |
|---|
| Numbering: | Vol. 33, iss. 6 |
|---|
| PID: | 20.500.12556/DiRROS-18406  |
|---|
| UDC: | 517.5 |
|---|
| ISSN on article: | 1050-6926 |
|---|
| DOI: | 10.1007/s12220-023-01222-z |
|---|
| COBISS.SI-ID: | 147026947 |
|---|
| Note: | Spletna objava: 28. 3. 2023;
|
|---|
| Publication date in DiRROS: | 15.03.2024 |
|---|
| Views: | 442 |
|---|
| Downloads: | 225 |
|---|
| 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. |
