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arXiv · 2201.03334

Canonical parametrizations of metric surfaces of higher topology

Martin Fitzi·Damaris Meier
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Abstract

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 in a paper of Lytchak and Wenger.

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Martin Fitzi, Damaris Meier. 2022-01-10. Canonical parametrizations of metric surfaces of higher topology. https://arxiv.org/abs/2201.03334

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