Revista Matemática Iberoamericana
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Published online: 1996-12-31
The boundary absolute continuity of quasiconformal mappings IIJuha Heinonen (1) University of Michigan, Ann Arbor, USA
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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Heinonen Juha: The boundary absolute continuity of quasiconformal mappings II. Rev. Mat. Iberoamericana 12 (1996), 697-725. doi: 10.4171/RMI/212