Calculus of Variations and Geometric Measure Theory

R. Luisto - P. Pankka

Stoïlow's theorem revisited

created by luisto on 20 Dec 2018



Inserted: 20 dec 2018
Last Updated: 20 dec 2018

Year: 2017

ArXiv: 1701.05726 PDF

Acknowledgement for support from the GeoMeg project will appear in an upcoming version.


Sto\"ilow's theorem from 1928 states that a continuous, light, and open mapping between surfaces is a discrete map with a discrete branch set. This result implies that such mappings between orientable surfaces are locally modelled by power mappings $z\mapsto z^k$ and admit a holomorphic factorization. The purpose of this expository article is to give a proof of this classical theorem having the readers interested in discrete and open mappings in mind.

Tags: GeoMeG