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.
1
Kantonsschule Heerbrugg
2
University of Fribourg, Department of Mathematics
Martin Fitzi; Damaris Meier. Canonical parametrizations of metric surfaces of higher topology. Annales Fennici Mathematici, Tome 48 (2023) no. 1, pp. 67-80. doi: 10.54330/afm.125076
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