Second main theorem and uniqueness problem of meromorphic mappings with moving hypersurfaces

TL;DR

This paper develops new second main theorems for meromorphic mappings into projective space with moving hypersurfaces, and proves a uniqueness theorem for mappings sharing few hypersurfaces, extending previous results and considering algebraic degeneracy.

Contribution

It introduces improved second main theorems involving truncated counting functions and establishes a novel uniqueness theorem for meromorphic mappings sharing moving hypersurfaces without multiplicity.

Findings

Established new second main theorems with truncated counting functions.

Proved a uniqueness theorem for meromorphic mappings sharing few moving hypersurfaces.

Extended results to include algebraically degenerate mappings.

Abstract

In this article, we establish some new second main theorems for meromorphic mappings of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ and moving hypersurfaces with truncated counting functions. A uniqueness theorem for these mappings sharing few moving hypersurfaces without counting multiplicity is also given. This result is an improvement of the recent result of Dethloff - Tan [3]. Moreover the meromorphic mappings in our result may be algebraically degenerate. The last purpose of this article is to study uniqueness problem in the case where the meromorphic mappings agree on small identical sets.