Existence of harmonic coordinates on general sub-Riemannian manifolds

Establish whether every measured sub-Riemannian manifold admits harmonic coordinates, namely local coordinate systems whose coordinate functions are harmonic.

Background

The paper proves that harmonically homogeneous measured sub-Riemannian manifolds admit harmonic coordinates. It notes that the existence of harmonic coordinates without the harmonic homogeneity assumption is unresolved, and that such coordinates would provide a possible route to proving regularity of harmonic morphisms in full generality.