Geodesic
Uniformization of metric surfaces using isothermal coordinates
Toni Ikonen1
1University of Jyväskylä, Department of Mathematics and Statistics
Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 155-180

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  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.
DOI : 10.54330/afm.112781
Keywords: Quasiconformal, uniformization, surface, reciprocality, isothermal, approximate metric differential

Toni Ikonen  1

1 University of Jyväskylä, Department of Mathematics and Statistics 
Toni Ikonen. Uniformization of metric surfaces using isothermal coordinates. Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 155-180. doi: 10.54330/afm.112781
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