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 $\mathbb B^3 \rightarrow D$, 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 $n≥3$, showing that quasiconformal maps from the unit $n$-ball onto Jordan domains with boundary (n–1)-rectifiable need not have absolutely continuous boundary values.