The Landau-Bloch type theorems for certain class of holomorphic and pluriharmonic mappings in $\mathbb{c}^n$

TL;DR

This paper establishes Landau-Bloch type theorems and lower bounds for Bloch's constant for specific classes of holomorphic and pluriharmonic mappings in multi-dimensional complex space.

Contribution

It introduces new classes of holomorphic mappings and derives lower estimates for Bloch's constant and Landau-Bloch theorems in higher dimensions.

Findings

Lower estimates for Bloch's constant for the defined classes.

Landau-Bloch type theorems for subclasses of pluriharmonic mappings.

Results extend classical theorems to multi-dimensional complex spaces.

Abstract

In this paper, we first define two classes of holomorphic mappings defined on the unit ball $B^n$ of n-dimensional complex space $\mathbb{C}^n$ 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 $B^n$.