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 editorsRomney, Matthew

Journal or seriesAdvances in Mathematics

ISSN0001-8708

eISSN1090-2082

Publication year2019

Volume31

Issue number0

Pages range479-494

PublisherAcademic Press

Publication countryUnited Kingdom

Publication languageEnglish

DOIhttps://doi.org/10.1016/j.aim.2019.05.022

Publication open accessOther 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 availablehttps://arxiv.org/abs/1803.02322


Abstract

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.


Keywordscomplex analysismetric spaces

Free keywordsquasiconformal mapping; metric space; absolute continuity


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Ministry reportingYes

Reporting Year2019

JUFO rating3


Last updated on 2023-03-10 at 12:32