Editing Conformal map (section)

===Euclidean space===
A [[Liouville's theorem (conformal mappings)|classical theorem]] of [[Joseph Liouville]] shows that there are far fewer conformal maps in higher dimensions than in two dimensions. Any conformal map from an open subset of [[Euclidean space]] into the same Euclidean space of dimension three or greater can be composed from three types of transformations: a [[homothetic transformation|homothety]], an [[isometry]], and a [[special conformal transformation]]. For [[Linear map|linear transformations]], a conformal map may only be composed of [[homothetic transformation|homothety]] and [[isometry]], and is called a [[conformal linear transformation]].