Liouville's theorem (conformal mappings)

In mathematics, Liouville's theorem, proved by Joseph Liouville in 1850, is a rigidity theorem about conformal mappings in Euclidean space. It states that every smooth conformal mapping on a domain of Rn, where n > 2, can be expressed as a composition of translations, homotheties, orthogonal transformations and inversions: they are Möbius transformations (in n dimensions).

Source: Wikipedia — Liouville's theorem (conformal mappings) (CC BY-SA 4.0)