Construction of biholomorphic convex mappings on \(D_p\) in \(\mathbb{C}^n\)
type: Item
instance of: scholarly article
title: Construction of biholomorphic convex mappings on \(D_p\) in \(\mathbb{C}^n\)
zbMATH Open document ID: 1181.32020
DOI: 10.1216/RMJ-2009-39-3-853
author: Ming-Sheng Liu
author: Yucan Zhu
published in: Rocky Mountain Journal of Mathematics
publication date: 2009-06-18T00:00:00Z
review text: The authors are concerned with various sufficient conditions for convexity of biholomorphic mappings on the Reinhardt domain \(D_p=\{(z_1,\dots,z_n)\in\mathbb{C}^n: \sum_{j=1}^n|z_j|^{p_j}<1\}\), where \(p_j>1\) for \(j=1,\dots,n\). Concrete examples of convex (biholomorphic) mappings on \(D_p\) are also provided. Their results are generalizations of previous results due to Yu-Can Zhu, J. Muir and T. J. Suffridge.
reviewed by: G. Kohr
Mathematics Subject Classification ID: 32H02
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 5566205
zbMATH Keywords: biholomorphic mapping
zbMATH Keywords: convex mapping
zbMATH Keywords: convex balanced domain
zbMATH Keywords: locally biholomorphic mapping
zbMATH Keywords: Minkowski functional
zbMATH Keywords: Reinhardt domain
MaRDI profile type: Publication
cites work: Q4211223
cites work: On the Roper-Suffridge extension operator.
cites work: The generalized Roper-Suffridge extension operator
cites work: Growth and covering theorems associated with the Roper-Suffridge extension operator
cites work: Extension operators for locally univalent mappings
cites work: Q4444884
cites work: Univalent mappings associated with the Roper-Suffridge extension operator
cites work: An Extension Theorem and Subclasses of Univalent Mappings in Several Complex Variables
cites work: Loewner chains and the Roper-Suffridge extension operator
cites work: On the generalized Roper-Suffridge extension operator in Banach spaces
cites work: On decomposition theorem of normalized biholomorphic convex mappings in Reinhardt domains
cites work: Construction of convex mappings of \(p\)-balls in \(\mathbb{C}^2\)
cites work: Convex mappings on the unit ball of \(\mathbb C^ n\)
cites work: Convexity properties of holomorphic mappings in ℂⁿ
cites work: Q3966611
cites work: Q4454011
cites work: Q4472775
cites work: Q5309659
cites work: The generalized Roper-Suffridge extension operator in Banach spaces. II.
description: scientific article; zbMATH DE number 5566205