Proper holomorphic maps in Euclidean spaces avoiding unbounded convex sets

Autor: Drnovsek, Barbara Drinovec, Forstneric, Franc
Rok vydání: 2023
Předmět:
Zdroj: J. Geom. Anal., 33:170, 2023
Druh dokumentu: Working Paper
DOI: 10.1007/s12220-023-01222-z
Popis: 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 holomorphic maps $f:X\to \mathbb C^n$ from any Stein manifold $X$ of dimension $Comment: Research supported by the European Union (ERC Advanced grant HPDR, 101053085 to Franc Forstneric) and grants P1-0291, J1-3005, N1-0137 and N1-0237 from ARRS, Republic of Slovenia
Databáze: arXiv