We use the recently established existence and regularity of area and energy minimizing disks in metric spaces to obtain canonical parameterizations of metric surfaces. Our approach yields a new and conceptually simple proof of a well-known theorem of Bonk and Kleiner on the existence of quasisymmetric parameterizations of linearly locally connected, Ahlfors -regular metric -spheres. Generalizations and applications to the geometry of such surfaces are described.
"Canonical parameterizations of metric disks." Duke Math. J. 169 (4) 761 - 797, 15 March 2020. https://doi.org/10.1215/00127094-2019-0065