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
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American Journal of MathematicsDate
2021Copyright
© 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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European Commission; Academy of FinlandFunding program(s)
Academy Research Fellow, AoF
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.
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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.License
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