The boundary absolute continuity of quasiconformal mappings II

Abstract

In this paper a quite complete picture is given of the absolute continuity on the boundary of a quasiconformal map ${\mathbb{B}}^3\to D$, where ${\mathbb{B}}^3$ is the unit 3-ball and $D$ is a Jordan domain in ${\mathbb{R}}^3$ with boundary rectifiable in the sense of geometric measure theory. Moreover, examples are constructed for each $n\ge 3$, showing that quasiconformal maps from the unit $n$-ball onto Jordan domains with boundary $(n–1)$-rectifiable need not have absolutely continuous boundary values.