Answer by user88196 for Is there an underlying explanation for the magical powers of the Schwarzian derivative?

One very simple interpretation is possible, if I am not mistaken:

Characterizing conformal nets, or more general harmonic nets having in mindthe lift to minimal surfaces, it turns out thatthere exists a simple uniform relationship of four fundamental entities upto normalization for orthogonal trajectories:

1. The sum of the changes of geodesic curvature is zero.

2. The difference of the changes of geodesic curvature is the realpart of the Schwarzian derivative.

3. The difference of the changes of geodesic acceleration is theimaginary part of the Schwarzian derivative.

4. The sum of the changes of geodesic acceleration is the Gaussiancurvature.

http://vixra.org/abs/1301.0071