JournalsrmiVol. 12, No. 3pp. 697–725

The boundary absolute continuity of quasiconformal mappings II

  • Juha Heinonen

    University of Michigan, Ann Arbor, USA
The boundary absolute continuity of quasiconformal mappings II cover
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Abstract

In this paper a quite complete picture is given of the absolute continuity on the boundary of a quasiconformal map B3D\mathbb B^3 \rightarrow D, where B3\mathbb B^3 is the unit 3-ball and DD is a Jordan domain in R3\mathbb R^3 with boundary rectifiable in the sense of geometric measure theory. Moreover, examples are constructed for each n3n≥3, showing that quasiconformal maps from the unit nn-ball onto Jordan domains with boundary (n–1)-rectifiable need not have absolutely continuous boundary values.

Cite this article

Juha Heinonen, The boundary absolute continuity of quasiconformal mappings II. Rev. Mat. Iberoam. 12 (1996), no. 3, pp. 697–725

DOI 10.4171/RMI/212