2022

Ikonen, Toni

We establish a uniformization result for metric surfaces—metric spaces that aretopological surfaces with locally finite Hausdorff2-measure. Using the geometric definition of qua-siconformality, we show that a metric surface that can be covered by quasiconformal images ofEuclidean domains is quasiconformally equivalent to a Riemannian surface. To prove this, weconstruct an atlas of suitable isothermal coordinates.