On the inverse absolute continuity of quasiconformal mappings on hypersurfaces
Ntalampekos, D., & Romney, M. (2021). On the inverse absolute continuity of quasiconformal mappings on hypersurfaces. American Journal of Mathematics, 143(5), 1633-1659. https://doi.org/10.1353/ajm.2021.0041
Julkaistu sarjassa
American Journal of MathematicsPäivämäärä
2021Tekijänoikeudet
© 2021 by Johns Hopkins University Press
We construct quasiconformal mappings f:R3→R3 for which there is a Borel set E⊂R2×{0} of positive Lebesgue 2-measure whose image f(E) has Hausdorff 2-measure zero. This gives a solution to the open problem of inverse absolute continuity of quasiconformal mappings on hypersurfaces, attributed to Gehring. By implication, our result also answers questions of V\"ais\"al\"a and Astala--Bonk--Heinonen.
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Johns Hopkins University PressISSN Hae Julkaisufoorumista
0002-9327Asiasanat
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https://converis.jyu.fi/converis/portal/detail/Publication/101958606
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Rahoittaja(t)
Euroopan komissio; Suomen AkatemiaRahoitusohjelmat(t)
Akatemiatutkija, SA
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Lisätietoja rahoituksesta
Research of the first author supported in part by NSF grant DMS-1506099; research of the second author supported by the Academy of Finland grant 288501 and by the ERC Starting grant 713998 GeoMeG.Lisenssi
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