THE IMPACT OF THE RIEMANN MAPPING THEOREM ON ANALYTIC STRUCTURE IN THE THEORY OF COMPLEX FUNCTIONS

Abstract

This article explores the influence of the Riemann Mapping Theorem on the development of analytic structures within the field of complex function theory. By providing a powerful tool for conformal mapping, the Riemann Mapping Theorem has played a pivotal role in bridging topological properties with analytic functions, allowing for the simplification and standardization of domains in complex analysis. The article discusses the theorem’s foundational importance in transforming simply connected domains into the unit disk, enabling the generalization of classical results and facilitating practical applications in both theoretical and applied mathematics. Through a comprehensive review of mathematical developments and methodological advancements, the study emphasizes how the theorem has contributed to the conceptual and structural evolution of modern complex analysis, particularly in the context of teaching and research within higher mathematical education.