Let F be an arbitrary class of continuous mappings acting and ranging on domains in Rnwhich is invariant under similarity transformations of Rnand the restriction of a map to any subdomain. The class Mob of Möbius mappings acting in Rnis of particular interest. Assume that the class F is “c-uniformly close” to Möb. Then we show that any map in F is either constant or a local quasiconformal homeomorphism. As a corollary we obtain a distinctly elementary proof of the Local Injectivity Theorem for quasiregular mappings.
ASJC Scopus subject areas
- Applied Mathematics