Higher-dimensional Euclidean Space
A classical theorem of Joseph Liouville called Liouville's theorem shows the higher-dimensions have less varied conformal maps:
Any conformal map on a portion of Euclidean space of dimension greater than 2 can be composed from three types of transformation: a homothetic transformation, an isometry, and a special conformal transformation. (A special conformal transformation is the composition of a reflection and an inversion in a sphere.) Thus, the group of conformal transformations in spaces of dimension greater than 2 are much more restricted than the planar case, where the Riemann mapping theorem provides a large group of conformal transformations.
Read more about this topic: Conformal Map
Famous quotes containing the word space:
“Play is a major avenue for learning to manage anxiety. It gives the child a safe space where she can experiment at will, suspending the rules and constraints of physical and social reality. In play, the child becomes master rather than subject.... Play allows the child to transcend passivity and to become the active doer of what happens around her.”
—Alicia F. Lieberman (20th century)