Some applications of universal holomorphic motions
type: Item
instance of: scholarly article
title: Some applications of universal holomorphic motions
zbMATH Open document ID: 1123.32008
author: Yunping Jiang
author: Sudeb Mitra
published in: Kodai Mathematical Journal
publication date: 2007-08-02T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.kmj/1175287624
review text: Let \(E\) be a closed subset of the extended complex plane \(\hat\mathbb C\). Then there is a contractible complex Banach manifold, known as the Teichmüller space \(T(E)\), which was first studied by [\textit{G. Lieb}, Ph. D. dissertation, Cornell University, (1990)]. The second author, of the paper under review, \textit{S. Mitra} [J. Anal. Math. 81, 1--33 (2000; Zbl 0966.32009)] proved that \(T(E)\) can be considered as the universal parameter space for holomorphic motions of the closed set \(E\) over a simply connected complex Banach manifold. This universal property has found several applications to the study of holomorphic motions. In this paper, the authors give some new applications of this universal property to the study of holomorphic motions and holomorphic dynamical systems.
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 37F30
Mathematics Subject Classification ID: 37F45
zbMATH DE Number: 5176716
zbMATH Keywords: holomorphic motion
zbMATH Keywords: Teichmüller space
zbMATH Keywords: Julia set
reviewed by: Yuliang Shen
MaRDI profile type: Publication
OpenAlex ID: W2089974715
DOI: 10.2996/KMJ/1175287624
description: scientific article