On the inverse absolute continuity of quasiconformal mappings on hypersurfaces

Dimitrios Ntalampekos, Matthew Romney

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)1633-1659
Number of pages27
JournalAmerican Journal of Mathematics
Volume143
Issue number5
DOIs
StatePublished - Oct 2021

Fingerprint

Dive into the research topics of 'On the inverse absolute continuity of quasiconformal mappings on hypersurfaces'. Together they form a unique fingerprint.

Cite this