On Riemann's mapping theorem

TL;DR

This paper presents a new proof of Riemann's mapping theorem and proposes a method that could extend the theorem's principles to three-dimensional cases.

Contribution

It introduces a novel proof technique for Riemann's theorem and suggests an approach for its generalization to higher dimensions.

Findings

New proof of Riemann's mapping theorem

Proposed method for three-dimensional analog

Potential extension to higher dimensions

Abstract

In this paper we give a new proof of Riemann's well known mapping theorem. The suggested method permits to prove an analog of that theorem for the three dimensional case.