Quasiregular map

Summary

A quasiregular map is a map between domains of $\R^n$ whose infinitesimal distortion is bounded. It sends small balls to sets that are round up to a fixed factor. Unlike a quasiconformal map, it need not be injective, so it generalizes holomorphic functions rather than conformal maps. In the plane, quasiregular maps are holomorphic functions composed with quasiconformal homeomorphisms. In dimension $n \ge 3$ they give a rich substitute for holomorphic functions, since conformal maps there are only Möbius maps.