Hyperbolicity of circular domains
type: Item
instance of: scholarly article
title: Hyperbolicity of circular domains
zbMATH Open document ID: 0554.32020
author: Kazuo Azukawa
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1983-01-01T00:00:00Z
review text: A domain \(D\subset {\mathbb{C}}^ n\) is called strictly starlike circular if D contains the origin and \((i)\quad \lambda D\subset D\) for all \(\lambda\in {\mathbb{C}}\) with \(| \lambda | \leq 1\), (ii) closure \(\bar D\subset \lambda D\) for any real \(\lambda >1\). It is proved that if every \({\mathbb{C}}\)-linear map from \({\mathbb{C}}\) to D is zero, then D is bounded and consequently is hyperbolic in Kobayashi sense. It is given an example of pseudoconvex circular domain in \({\mathbb{C}}^ 2\) which contains no entire holomorphic curve and is not hyperbolic.
Mathematics Subject Classification ID: 32Q45
Mathematics Subject Classification ID: 32T99
Mathematics Subject Classification ID: 32A07
zbMATH DE Number: 3882735
zbMATH Keywords: hyperbolicity
zbMATH Keywords: Kobayashi distance
zbMATH Keywords: Schwartz lemma
zbMATH Keywords: strictly starlike circular domain
zbMATH Keywords: pseudoconvex circular domain
reviewed by: A. N. Parshin
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228999
OpenAlex ID: W2013889731
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DOI: 10.2748/TMJ/1178228999
description: scientific article; zbMATH DE number 3882735