Stability property of möbius mappings

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)61-69
Number of pages9
JournalProceedings of the American Mathematical Society
Volume100
Issue number1
DOIs
StatePublished - May 1987

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ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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