TY - JOUR
AU - Fitzi, Martin
AU - Meier, Damaris
PY - 2022/12/02
Y2 - 2023/02/08
TI - Canonical parametrizations of metric surfaces of higher topology
JF - Annales Fennici Mathematici
JA - Ann. Fenn. Math.
VL - 48
IS - 1
SE - Articles
DO - 10.54330/afm.125076
UR - https://afm.journal.fi/article/view/125076
SP - 67-80
AB - <p> </p><pre>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.</pre>
ER -