Canonical parametrizations of metric surfaces of higher topology
Avainsanat:
Uniformization theorem, quasisymmetric homeomorphism, metric spaces, Sobolev mapsAbstrakti
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.
Viittaaminen
Fitzi, M., & Meier, D. (2022). Canonical parametrizations of metric surfaces of higher topology. Annales Fennici Mathematici, 48(1), 67–80. https://doi.org/10.54330/afm.125076
Copyright (c) 2022 Annales Fennici Mathematici
Tämä työ on lisensoitu Creative Commons Nimeä-EiKaupallinen 4.0 Kansainvälinen Julkinen -lisenssillä.