
## 3. Uniformization and parameterization

1. ### Bi-Lipschitz 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 bi-Lipschitz 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.
• ### Bi-Lipschitz 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 bi-Lipschitz map.

Cite this as: AimPL: Mapping theory in metric spaces, available at http://aimpl.org/mappingmetric.