Mappings of finite distortion: A new proof for discreteness and openness

Jani Onninen; Xiao Zhong

doi:10.1017/S0308210506000825

Mappings of finite distortion: A new proof for discreteness and openness

Jani Onninen, Xiao Zhong

Department of Mathematics

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

9 Scopus citations

Abstract

We give a new and elementary proof of the known result: a non-constant mapping of finite distortion f:ω ⊂ ℝⁿ → ℝⁿ is discrete and open, provided that its distortion function K ∈ L¹loc(Ω) if n = 2 and that K ∈ L^ploc (Ω) for some p > n - 1 if n ≥ 3.

Original language	English (US)
Pages (from-to)	1097-1102
Number of pages	6
Journal	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume	138
Issue number	5
DOIs	https://doi.org/10.1017/S0308210506000825
State	Published - Oct 2008

ASJC Scopus subject areas

General Mathematics

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abstract = "We give a new and elementary proof of the known result: a non-constant mapping of finite distortion f:ω ⊂ ℝn → ℝn is discrete and open, provided that its distortion function K ∈ L1loc(Ω) if n = 2 and that K ∈ Lploc (Ω) for some p > n - 1 if n ≥ 3.",

author = "Jani Onninen and Xiao Zhong",

note = "Funding Information: J.O. was supported by the National Science Foundation Grant no. DMS-0400611 and X.Z. was supported by the Academy of Finland, Project no. 207288.",

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AU - Zhong, Xiao

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N2 - We give a new and elementary proof of the known result: a non-constant mapping of finite distortion f:ω ⊂ ℝn → ℝn is discrete and open, provided that its distortion function K ∈ L1loc(Ω) if n = 2 and that K ∈ Lploc (Ω) for some p > n - 1 if n ≥ 3.

AB - We give a new and elementary proof of the known result: a non-constant mapping of finite distortion f:ω ⊂ ℝn → ℝn is discrete and open, provided that its distortion function K ∈ L1loc(Ω) if n = 2 and that K ∈ Lploc (Ω) for some p > n - 1 if n ≥ 3.

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Mappings of finite distortion: A new proof for discreteness and openness

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