### Abstract

Let F be an arbitrary class of continuous mappings acting and ranging on domains in R_{n}which is invariant under similarity transformations of R_{n}and the restriction of a map to any subdomain. The class Mob of Möbius mappings acting in R_{n}is 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.

Original language | English (US) |
---|---|

Pages (from-to) | 61-69 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 100 |

Issue number | 1 |

DOIs | |

State | Published - May 1987 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics