Uniformization of metric surfaces using isothermal coordinates
Nyckelord:
Quasiconformal, uniformization, surface, reciprocality, isothermal, approximate metric differentialAbstract
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.
Referera så här
Ikonen, T. (2021). Uniformization of metric surfaces using isothermal coordinates. Annales Fennici Mathematici, 47(1), 155–180. https://doi.org/10.54330/afm.112781
Copyright (c) 2021 Annales Fennici Mathematici
Detta verk är licensierat under en Creative Commons Erkännande-IckeKommersiell 4.0 Internationell-licens.