Beltrami coefficient (${\mu }_f=f_{\bar{z}}/f_z$)

For an orientation-preserving quasiconformal map, the almost-everywhere coefficient ${\mu }_f=f_{\bar{z}}/f_z$. It is a coordinate-dependent representative of a tensor; the modulus and the resulting maximal dilatation are coordinate-independent.

The equation $f_{\bar{z}}=\mu f_z$ prescribing the Beltrami coefficient of a quasiconformal map. Two homeomorphic solutions on the same source differ by a biholomorphism between their targets.