The Bloch theorem in several complex variables

DOI10.1007/BF02921592zbMath0794.32006OpenAlexW2014918614MaRDI QIDQ1323553

Carl H. FitzGerald, Sheng Gong

Publication date: 10 July 1994

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02921592

zbMATH Keywords

Bergman kernel functionclassical domainsBloch's constant

Mathematics Subject Classification ID

Related Items (13)

Distortion of locally biholomorphic Bloch mappings on bounded symmetric domains ⋮ Landau-Bloch constants for functions in \(\alpha\)-Bloch spaces and Hardy spaces ⋮ The Roper-Suffridge extension operator and its applications to convex mappings in ${\mathbb {C}}^{2}$ ⋮ Bloch Mappings on Bounded Symmetric Domains ⋮ Bloch constants in several variables ⋮ Bloch constant of holomorphic mappings on the unit ball of \(\mathbb C^n\) ⋮ Bloch constant of holomorphic mappings on the unit polydisk of \(\mathbb C^n\) ⋮ \(\alpha\)-Bloch mappings on bounded symmetric domains in \(\mathbb C^n\) ⋮ A Landau's theorem in several complex variables ⋮ A distortion theorem and the Bloch constant for Bloch mappings in \(\mathbb{C}^N\) ⋮ Pluriharmonic mappings in \(\mathbb{C}^n\) and complex Banach spaces ⋮ Distortion theorems on the Lie ball \({\mathcal R}_{\mathrm{IV}} (n)\) in \(\mathbb C^{n }\) ⋮ Distortion theorem for Bloch mappings on the unit ball \(\mathcal B^n\)

Cites Work

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• Bloch functions of several complex variables
• On the size of balls covered by analytic transformations
• Bloch's theorem for meromorphic functions
• On Bloch's Constant
• Bloch Functions in Several Complex Variables, I
• Distortion Theorems for Bloch Functions
• Quantitative Bloch's theorem for certain classes of holomorphic mappings of the ball into Pn (C).
• Higher Dimensional Generalizations of the Bloch Constant and their Lower Bounds
• Holomorphic Mappings of the Hyperbolic Space into the Complex Euclidean Space and the Bloch Theorem
• An Extension of Schwarz's Lemma
• Bloch’s theorem for real variables
• Normal families of holomorphic mappings

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