Norm order and geometric properties of holomorphic mappings in \(\mathbb{C}^n\)

DOI10.1007/BF02791231zbMath0978.32017OpenAlexW2011927010MaRDI QIDQ5926439

Ted J. Suffridge, John A. Pfaltzgraff

Publication date: 28 February 2001

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02791231

zbMATH Keywords

growthconvexitycovering theoremlinear distortionlinear invariant familylocally biholomorphic mappingsstarlikenessunivalence

Mathematics Subject Classification ID

Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables (32H02)

Related Items (26)

Construction of convex mappings of \(p\)-balls in \(\mathbb{C}^2\) ⋮ Growth and two-point distortion for biholomorphic mappings of the ball ⋮ The subordination principle and its application to the generalized Roper-Suffridge extension operator ⋮ The Roper-Suffridge extension operator and classes of biholomorphic mappings ⋮ Horosphere-invariant mappings of the unit ball in \(\mathbb{C}^n\) ⋮ A Schwarz lemma at the boundary on complex Hilbert balls and applications to starlike mappings ⋮ Distortion theorems for normalized biholomorphic quasi-convex mappings ⋮ The Roper-Suffridge extension operator and its applications to convex mappings in ${\mathbb {C}}^{2}$ ⋮ Two generalizations of Bohr radius ⋮ Applications of a decomposition of holomorphic mappings in \(\mathbb C^n\) with respect to a cyclic group ⋮ Linear invariance of locally biholomorphic mappings in the unit ball of a JB\(^\ast\)-triple ⋮ Koebe invariant functions and extremal problems for holomorphic mappings in the unit ball of \(\mathbb C^n\) ⋮ Convex families of holomorphic mappings related to the convex mappings of the ball in $\mathbb {C}^n$ ⋮ Two-point distortion bounds for biholomorphic mappings of the ball in \(\mathbb C^n\) ⋮ Distortion and covering theorems of pluriharmonic mappings ⋮ Relations among starlikeness, convexity and \(k\)-fold symmetry of locally biholomorphic mappings in \(\mathbb{C}^n\) ⋮ Extreme points for convex mappings of \(B_n \) ⋮ Growth and distortion theorems for linearly invariant families on homogeneous unit balls in \(\mathbb C^n\) ⋮ Roper-Suffridge extension operator and the lower bound for the distortion ⋮ Trace-order and a distortion theorem for linearly invariant families on the unit ball of a finite dimensional JB\(^{\ast }\) -triple ⋮ Distortion theorems for convex mappings on homogeneous balls ⋮ Two-point distortion theorems for harmonic and pluriharmonic mappings ⋮ On two conjectures for convex biholomorphic mappings in \(\mathbb C ^n\) ⋮ A generalization of half-plane mappings to the ball in ℂⁿ ⋮ The growth, covering and distortion theorems for a subclass of convex mappings ⋮ Distortion theorems for biholomorphic convex mappings in \({\mathbb C}^n\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some bounds on convex mappings in several complex variables
• Linear-invariante Familien analytischer Funktionen. I
• Linear spaces and linear-invariant families of locally univalent analytic functions
• Starlike and convex mappings in several complex variables
• Starlike and convex maps in Banach spaces
• An Extension Theorem and Subclasses of Univalent Mappings in Several Complex Variables
• Linear invariance and uniform local univalence
• Distortion of locally biholomorphic maps of the N-Ball
• Subordination chains and quasiconformal extension of holomorphic maps in C^n
• Convexity properties of holomorphic mappings in ℂⁿ
• A Distortion Theorem for Biholomorphic Mappings in ℂ 2
• Linear Invariance, Order and Convex Maps in
• On a theorem of Grace

This page was built for publication: Norm order and geometric properties of holomorphic mappings in \(\mathbb{C}^n\)