Uniformization of metric surfaces using isothermal coordinates

Authors

  • Toni Ikonen University of Jyväskylä, Department of Mathematics and Statistics

Keywords:

Quasiconformal, uniformization, surface, reciprocality, isothermal, approximate metric differential

Abstract

 

We establish a uniformization result for metric surfaces – metric spaces that are topological surfaces with locally finite Hausdorff 2-measure. Using the geometric definition of quasiconformality, we show that a metric surface that can be covered by quasiconformal images of Euclidean domains is quasiconformally equivalent to a Riemannian surface. To prove this, we construct an atlas of suitable isothermal coordinates.
Section
Articles

Published

2021-12-13

How to Cite

Ikonen, T. (2021). Uniformization of metric surfaces using isothermal coordinates. Annales Fennici Mathematici, 47(1), 155–180. https://doi.org/10.54330/afm.112781