Proper holomorphic discs avoiding closed convex sets
type: Item
instance of: scholarly article
title: Proper holomorphic discs avoiding closed convex sets
zbMATH Open document ID: 1018.32021
author: Barbara Drinovec Drnovšek
published in: Mathematische Zeitschrift
publication date: 2003-03-27T00:00:00Z
review text: The following result is proved. Let \(\Delta\) be the open unit disc in \(\mathbb{C}\). Let \(C\) be a closed convex subset of \(\mathbb{C}^2\). Then, for any point \(p\in\mathbb{C}^2 \setminus C\) there exists a proper holomorphic map \(\varphi:\Delta \to\mathbb{C}^2\) with \(\varphi(0)=p\) and \(\varphi(\Delta)\cap C= \emptyset\) if and only if either \(C\) is a complex line or \(C\) does not contain any complex line.
Mathematics Subject Classification ID: 32H35
zbMATH DE Number: 1889151
zbMATH Keywords: proper holomorphic disc
zbMATH Keywords: convex set
zbMATH Keywords: proper holomorphic map
reviewed by: Viorel Vâjâitu
MaRDI profile type: Publication
full work available at URL: s00209-002-0433-7
OpenAlex ID: W1994215914
DOI: 10.1007/S00209-002-0433-7
description: scientific article; zbMATH DE number 1889151