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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Stability property of Möbius mappings


Author: T. Iwaniec
Journal: Proc. Amer. Math. Soc. 100 (1987), 61-69
MSC: Primary 30C60
DOI: https://doi.org/10.1090/S0002-9939-1987-0883402-2
MathSciNet review: 883402
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Abstract: Let $F$ be an arbitrary class of continuous mappings acting and ranging on domains in ${{\mathbf {R}}^n}$ which is invariant under similarity transformations of ${{\mathbf {R}}^n}$ and the restriction of a map to any subdomain. The class Möb of Möbius mappings acting in ${{\mathbf {R}}^n}$ 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.


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Article copyright: © Copyright 1987 American Mathematical Society