Stability property of möbius mappings

T. Iwaniec

doi:10.1090/S0002-9939-1987-0883402-2

Stability property of möbius mappings

T. Iwaniec

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Let F be an arbitrary class of continuous mappings acting and ranging on domains in R_nwhich is invariant under similarity transformations of R_nand the restriction of a map to any subdomain. The class Mob of Möbius mappings acting in R_nis 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	https://doi.org/10.1090/S0002-9939-1987-0883402-2
State	Published - May 1987

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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title = "Stability property of m{\"o}bius mappings",

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 M{\"o}bius mappings acting in Rnis of particular interest. Assume that the class F is “c-uniformly close” to M{\"o}b. 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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AB - 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.

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Stability property of möbius mappings

Abstract

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