Construction of biholomorphic convex mappings on \(D_p\) in \(\mathbb{C}^n\)

DOI10.1216/RMJ-2009-39-3-853zbMath1181.32020MaRDI QIDQ1024972

Yu-Can Zhu, Ming-Sheng Liu

Publication date: 18 June 2009

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Minkowski functionalReinhardt domainbiholomorphic mappingconvex mappinglocally biholomorphic mappingconvex balanced domain

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables (32H02)

Related Items (2)

Quasi-convex mappings of order \(\alpha\) on the unit polydisk in \(\mathbb{C}^n\) ⋮ On the biholomorphic convex mappings of order alpha on \(D_p^n\)

Cites Work

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• On decomposition theorem of normalized biholomorphic convex mappings in Reinhardt domains
• Extension operators for locally univalent mappings
• On the Roper-Suffridge extension operator.
• Loewner chains and the Roper-Suffridge extension operator
• Univalent mappings associated with the Roper-Suffridge extension operator
• The generalized Roper-Suffridge extension operator in Banach spaces. II.
• Construction of convex mappings of \(p\)-balls in \(\mathbb{C}^2\)
• Convex mappings on the unit ball of \(\mathbb C^ n\)
• On the generalized Roper-Suffridge extension operator in Banach spaces
• An Extension Theorem and Subclasses of Univalent Mappings in Several Complex Variables
• Convexity properties of holomorphic mappings in ℂⁿ
• Growth and covering theorems associated with the Roper-Suffridge extension operator
• The generalized Roper-Suffridge extension operator

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