A Uniformisation of Weighted Maps on Compact Surfaces

TL;DR

This paper discusses a method to uniformize weighted maps on compact surfaces, focusing on circle packings across surfaces of any genus, contributing to the understanding of geometric structures on complex surfaces.

Contribution

It introduces a uniformization approach for weighted maps on compact surfaces, extending circle packing theory to surfaces of arbitrary genus.

Findings

Established a uniformization method for weighted maps

Extended circle packing results to higher genus surfaces

Provided theoretical foundations for geometric structures on complex surfaces

Abstract

This article is a comprised version of my doctoral thesis defended at Basel University in 1995. It concerns circle packings on compact surfaces of any genus.