3. Uniformization and parameterization

BiLipschitz parameterization by Euclidean spaces
Problem 3.1.
[Yi Wang] Are there higher dimensional analogs of the Bonk–Lang parameterization theorem which give quantitative control on biLipschitz constants? 
Quasisymmetric uniformization of metric $2$spheres
Problem 3.2.
Give a geometric characterization of metric $2$spheres which are quasisymmetrically equivalent to the standard $2$sphere. 
BiLipschitz parameterization of metric $2$spheres
Problem 3.3.
Give a geometric characterization of metric $2$spheres which are equivalent to the standard $2$sphere via a biLipschitz map.
Cite this as: AimPL: Mapping theory in metric spaces, available at http://aimpl.org/mappingmetric.