Quasicircles modulo bilipschitz maps
A class \(S\) of explicit planar quasiconformal Jordan curves is constructed such that every quasicircle is a bilipshitz image of a curve in \(S\). The construction of a curve in \(S\) is similar to the von Koch snowflake curve except that there are two replacement options at each stage. This construction relies on the construction of a uniformly doubling probability measure bounded above by an \(\alpha\)-dimensional Hausdorff content, \(\alpha<2\), for a similar construction see [\textit{S. Konyagin} and \textit{A. Volberg}, Math. USSR., Izv. 30, No. 3, 629-638 (1988; Zbl 0727.28012)]. Bilipshitz homogeneous Jordan curves and Jacobians of planar quasiconformal mappings are also discussed.
scientific article; zbMATH DE number 1802557