2019/09/19 by Ikonen, Toni · 1 citation
#28A75 #51F99 #52A38 #Complex Variables (math.CV) #FOS: Mathematics #Metric Geometry (math.MG) #Primary 30L10 #Secondary 30C65
paper · doi:10.48550/arxiv.1909.09113
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 suitable isothermal coordinates.