A1 Journal article (refereed)
Singular quasisymmetric mappings in dimensions two and greater (2019)

Romney, M. (2019). Singular quasisymmetric mappings in dimensions two and greater. Advances in Mathematics, 31, 479-494. https://doi.org/10.1016/j.aim.2019.05.022

JYU authors or editors

Publication details

All authors or editors: Romney, Matthew

Journal or series: Advances in Mathematics

ISSN: 0001-8708

eISSN: 1090-2082

Publication year: 2019

Volume: 31

Issue number: 0

Pages range: 479-494

Publisher: Academic Press

Publication country: United Kingdom

Publication language: English

DOI: https://doi.org/10.1016/j.aim.2019.05.022

Publication open access: Other way freely accessible online

Publication channel open access:

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/64478

Web address where publication is available: https://arxiv.org/abs/1803.02322


For all n ≥2, we construct a metric space (X, d)and a quasisymmetric mapping f:[0, 1]n→X with the property that f−1 is not absolutely continuous with respect to the Hausdorff n-measure on X. That is, there exists a Borel set E⊂[0, 1]n with Lebesgue measure |E| >0 such that f(E) has Hausdorff n-measure zero. The construction may be carried out so that X has finite Hausdorff n-measure and |E| is arbitrarily close to 1, or so that |E| =1. This gives a negative answer to a question of Heinonen and Semmes.

Keywords: complex analysis; metric spaces

Free keywords: quasiconformal mapping; metric space; absolute continuity

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Ministry reporting: Yes

Reporting Year: 2019

JUFO rating: 3

Last updated on 2023-10-01 at 13:34