The Riemann mapping theorem from Riemann's viewpoint

This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.Comment: 14 pages, 2 figure

Bergman and Caratheodory metrics of the Kohn-Nirenberg domains

The Kohn-Nireberg domains are unbounded domains in the complex Euclidean space of dimension 2 upon which many outstanding questions are yet to be explored. The primary aim of this article is to demonstrate that the Bergman and Caratheodory metrics of any Kohn-Nirenberg domains are positive and complete.Comment: 11 page