Classification of rational holomorphic maps from \(\mathbb{B}^2\) into \(\mathbb{B}^\mathbb{N}\) with degree 2
type: Item
instance of: scholarly article
title: Classification of rational holomorphic maps from \(\mathbb{B}^2\) into \(\mathbb{B}^\mathbb{N}\) with degree 2
zbMATH Open document ID: 1211.32009
author: Yuan Zhang
author: Shanyu Ji
published in: Science in China. Series A
publication date: 2010-07-24T00:00:00Z
review text: Let Prop\(({\mathbf B}^n, {\mathbf B}^N)\) be the space of proper holomorphic mappings from the unit ball \({\mathbf B}^n\subset {\mathbb C}^n\) into the unit ball \({\mathbf B}^N\subset {\mathbb C}^N\), and let \(\text{Rat}({\mathbf B}^n, {\mathbf B}^N)=\text{Prop}({\mathbf B}^n, {\mathbf B}^N) \cap \{\text{rational\,\, maps}\}\). The authors are concerned with the classification problem for mappings in \(\text{Rat}({\mathbf B}^2, {\mathbf B}^N)\) with degree \(2\). The main result of the paper is contained in Theorem 1.1 in that the authors provide a complete description for mappings in \(\text{Rat}({\mathbf B}^2, {\mathbf B}^N)\) with degree \(2\). Particular cases are also presented.
reviewed by: G. Kohr
Mathematics Subject Classification ID: 32H02
zbMATH DE Number: 5760400
zbMATH Keywords: Cayley transformation
zbMATH Keywords: Heisenberg hypersurfaces
zbMATH Keywords: proper holomorphic map
zbMATH Keywords: rational holomorphic map
zbMATH Keywords: Siegel upper-half space
MaRDI profile type: Publication
full work available at URL: s11425-009-0147-y
OpenAlex ID: W2255957313
cites work: Rational holomorphic maps from \(\mathbb B^2\) into \(\mathbb B^N\) with degree 2
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cites work: On a semi-rigidity property for holomorphic maps
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cites work: Polynomial and rational maps between balls
DOI: 10.1007/S11425-009-0147-Y
description: scientific article; zbMATH DE number 5760400