The Riemann mapping theorem from Riemann's viewpoint

TL;DR

This paper provides a rigorous proof of the Riemann Mapping Theorem using Riemann's original method, avoiding reliance on topological intuition, thereby clarifying the theorem's foundational aspects.

Contribution

It offers a novel, purely analytical proof of the Riemann Mapping Theorem rooted in Riemann's approach, distinct from traditional topological methods.

Findings

Proof is based solely on analytical methods

Clarifies the foundational understanding of the theorem

Avoids topological assumptions in the proof

Abstract

This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.