On five papers by Herbert Gr{\"o}tzsch

TL;DR

This paper reviews five early works by Herbert Grötzsch, illustrating the development of his ideas from conformal to quasiconformal mappings and highlighting his contributions to Teichmüller theory.

Contribution

It provides a historical and mathematical overview of Grötzsch's foundational papers, emphasizing his motivation and results in quasiconformal mapping theory.

Findings

Progression from conformal to quasiconformal mappings

Introduction of quasiconformal mappings concepts

Influence on Teichmüller theory

Abstract

Herbert Gr{\"o}tzsch is the main founder of the theory of quasicon-formal mappings. We review five of his papers, written between 1928 and 1932, that show the progress of his work from conformal to quasiconformal geometry. This will give an idea of his motivation for introducing quasicon-formal mappings, of the problems he addressed and on the results he obtained concerning these mappings. The final version of this paper will appear in Vol. VII of the Handbook of Teichm{\"u}ller theory.