In this paper a quite complete picture is given of the absolute continuity on the boundary of a quasiconformal map , where is the unit 3-ball and is a Jordan domain in with boundary rectifiable in the sense of geometric measure theory. Moreover, examples are constructed for each , showing that quasiconformal maps from the unit -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. 697–725DOI 10.4171/RMI/212