Uniqueness theorems for meromorphic mappings sharing hyperplanes in general position

TL;DR

This paper establishes new uniqueness theorems for meromorphic mappings from complex Euclidean spaces to projective spaces, improving previous results by employing advanced methods for handling multiple values and sharing hyperplanes.

Contribution

It introduces two generalized uniqueness theorems for meromorphic mappings sharing hyperplanes, extending existing results in the field.

Findings

Two new general uniqueness theorems are proved.

The theorems improve and extend known results.

Methods involve advanced techniques for multiple values and hyperplane sharing.

Abstract

The purpose of this article is to study the uniqueness problem for meromorphic mappings from $\mathbb{C}^{n}$ into the complex projective space $\mathbb{P}^{N}(\mathbb{C}).$ By making using of the method of dealing with multiple values due to L. Yang and the technique of Dethloff-Quang-Tan respectively, we obtain two general uniqueness theorems which improve and extend some known results of meromorphic mappings sharing hyperplanes in general position.