A set containing rectifiable arcs QC-locally but not QC-globally

Christopher J. Bishop

doi:10.4310/PAMQ.2011.v7.n1.a7

A set containing rectifiable arcs QC-locally but not QC-globally

Christopher J. Bishop

Mathematics

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

13 Scopus citations

Abstract

We construct a Sierpinski carpet E ⊂ ℝ² of area zero and a K₀ > 1 with the property that every K₀-quasiconformal image of E contains rectifiable curves, but such that E has some quasiconformal image containing no non-constant rectifiable curves.

Original language	English
Pages (from-to)	121-138
Number of pages	18
Journal	Pure and Applied Mathematics Quarterly
Volume	7
Issue number	1
DOIs	https://doi.org/10.4310/PAMQ.2011.v7.n1.a7
State	Published - Jan 2011

Keywords

Jacobian problem
Quasiconformal mappings
Rectifiable curves
Sierpinski carpet

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10.4310/PAMQ.2011.v7.n1.a7

Cite this

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title = "A set containing rectifiable arcs QC-locally but not QC-globally",

abstract = "We construct a Sierpinski carpet E ⊂ ℝ2 of area zero and a K0 > 1 with the property that every K0-quasiconformal image of E contains rectifiable curves, but such that E has some quasiconformal image containing no non-constant rectifiable curves.",

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AB - We construct a Sierpinski carpet E ⊂ ℝ2 of area zero and a K0 > 1 with the property that every K0-quasiconformal image of E contains rectifiable curves, but such that E has some quasiconformal image containing no non-constant rectifiable curves.

KW - Jacobian problem

KW - Quasiconformal mappings

KW - Rectifiable curves

KW - Sierpinski carpet

UR - https://www.scopus.com/pages/publications/79952265933

U2 - 10.4310/PAMQ.2011.v7.n1.a7

DO - 10.4310/PAMQ.2011.v7.n1.a7

M3 - Article

AN - SCOPUS:79952265933

SN - 1558-8599

VL - 7

SP - 121

EP - 138

JO - Pure and Applied Mathematics Quarterly

JF - Pure and Applied Mathematics Quarterly

IS - 1

ER -

A set containing rectifiable arcs QC-locally but not QC-globally

Abstract

Keywords

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