TY - JOUR
T1 - On the inverse absolute continuity of quasiconformal mappings on hypersurfaces
AU - Ntalampekos, Dimitrios
AU - Romney, Matthew
N1 - Publisher Copyright:
© 2021 by Johns Hopkins University Press.
PY - 2021/10
Y1 - 2021/10
N2 - 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 Väisälä and Astala-Bonk-Heinonen.
AB - 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 Väisälä and Astala-Bonk-Heinonen.
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U2 - 10.1353/ajm.2021.0041
DO - 10.1353/ajm.2021.0041
M3 - Article
AN - SCOPUS:85111238571
SN - 0002-9327
VL - 143
SP - 1633
EP - 1659
JO - American Journal of Mathematics
JF - American Journal of Mathematics
IS - 5
ER -