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.
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