Summary of Thesis Doctor Mathematics: Some theorems on uniqueness and finiteness of meromorphic mappings

Some Theorems on Uniqueness and Finiteness of Meromorphic Mappings

Author: VANG’TY NOULORVANG

Field: Specialized: Geometry and Topology

Document Content:

This dissertation, titled “Some Theorems on Uniqueness and Finiteness of Meromorphic Mappings”, delves into the field of Value Distribution Theory and Complex Geometry. It aims to generalize and improve existing theorems related to the uniqueness and finiteness of meromorphic functions and mappings. The research focuses on extending theorems concerning the periodicity of meromorphic functions and exploring the uniqueness and algebraic dependence of meromorphic mappings in projective spaces. The work builds upon Nevanlinna theory and introduces new techniques to address these complex mathematical problems. The dissertation also contributes to the study of Picard’s theorem and the second main theorem for meromorphic mappings, particularly in cases involving shared values and truncated multiplicities.

Detailed Table of Contents:

• Introduction
• Chapter 1: Overview
• I. The uniqueness for the meromorphic function that has hyper order less than 1
• Chapter II. The uniqueness for the meromorphic function that has hyper degree less than 1
• Chapter III. The uniqueness for zero order meromorphic mapping
• Chapter IV. The algebraic degeneracy and finiteness of meromorphic mappings.