Canonical parametrizations of metric surfaces of higher topology


  • Martin Fitzi Kantonsschule Heerbrugg
  • Damaris Meier University of Fribourg, Department of Mathematics


Uniformization theorem, quasisymmetric homeomorphism, metric spaces, Sobolev maps



We give an alternate proof to the following generalization of the uniformization theorem by Bonk and Kleiner. Any linearly locally connected and Ahlfors 2-regular closed metric surface is quasisymmetrically equivalent to a model surface of the same topology. Moreover, we show that this is also true for surfaces as above with non-empty boundary and that the corresponding map can be chosen in a canonical way. Our proof is based on a local argument involving the existence of quasisymmetric parametrizations for metric discs as shown in a paper of Lytchak and Wenger.



How to Cite

Fitzi, M., & Meier, D. (2022). Canonical parametrizations of metric surfaces of higher topology. Annales Fennici Mathematici, 48(1), 67–80.