Proper holomorphic maps between balls of different dimensions
type: Item
instance of: scholarly article
title: Proper holomorphic maps between balls of different dimensions
zbMATH Open document ID: 0651.32014
author: John P. D'Angelo
published in: Michigan Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: The proper holomorphic mappings from the unit disc to itself are exactly the finite Blaschke products. On the unit ball \(B_ n\) in \({\mathbb{C}}^ n \)with \(n\geq 2\), any proper holomorphic self map is actually biholomorphic, i.e. an automorphism. It remains to classify the proper holomorphic maps from \(B_ n\) to \(B_ m\) for \(m>n\) (there aren't any for \(m<n).\) The present paper contains several results about polynomial proper maps. A one-parameter family of inequivalent proper maps from the n-ball to the 2n-ball is also given. The author then formulates a conjecture concerning ``factorization'' of proper maps from \(B_ n\) to \(B_ m\) into simple ones; this conjecture casts many known results on proper maps between balls into one framework. Finally, a list is given of all the monomial maps from the 2-ball to the 4-ball.
Mathematics Subject Classification ID: 32H35
Mathematics Subject Classification ID: 32A07
zbMATH DE Number: 4061637
zbMATH Keywords: proper holomorphic mappings
zbMATH Keywords: unit ball
zbMATH Keywords: polynomial proper maps
zbMATH Keywords: monomial maps
reviewed by: Emil J. Straube
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029003683
OpenAlex ID: W1588624094
DOI: 10.1307/MMJ/1029003683
description: scientific article; zbMATH DE number 4061637