The Landau-Bloch type theorems for certain class of holomorphic and pluriharmonic mappings in \mathbbcⁿ

2023/08/30 by Allu, Vasudeva Rao, Kumar, Rohit · 2 citations
#30C45 #30C50 #30C62 #31A05 #31C10 #32A18 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.15913

Abstract

In this paper, we first define two classes of holomorphic mappings defined on the unit ball Bⁿ of n-dimensional complex space ℂⁿ and obtain the lower estimates for Bloch's constant for these classes. Also, we derive the Landau-Bloch type theorem for some subclasses of pluriharmonic mappings defined on the unit ball Bⁿ.

Cited by

• Landau-type theorems for certain bounded poly-analytic and reduced poly-analytic functions
• Schwarz-Pick type lemma and Landau type theorem for α-harmonic mappings

Related

• Stable geometric properties of pluriharmonic and biholomorphic mappings, and Landau-Bloch's theorem
• Bloch and Landau type theorems for pluriharmonic mappings
• Equivalent moduli of continuity, Bloch's theorem for pluriharmonic mappings in \mathbbBⁿ
• Lipschitz continuity and composition operators in pluriharmonic Bloch spaces
• Weighted Lipschitz continuity, Schwarz-Pick's Lemma and Landau-Bloch's theorem for hyperbolic-harmonic mappings in ℂⁿ