The boundary absolute continuity of quasiconformal mappings (II).

Juha Heinonen

Revista Matemática Iberoamericana (1996)

  • Volume: 12, Issue: 3, page 697-725
  • ISSN: 0213-2230

Abstract

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In this paper a quite complete picture is given of the absolute continuity on the boundary of a quasiconformal map B3 → D, where B3 is the unit 3-ball and D is a Jordan domain in R3 with boundary 2-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.

How to cite

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Heinonen, Juha. "The boundary absolute continuity of quasiconformal mappings (II).." Revista Matemática Iberoamericana 12.3 (1996): 697-725. <http://eudml.org/doc/39521>.

@article{Heinonen1996,
abstract = {In this paper a quite complete picture is given of the absolute continuity on the boundary of a quasiconformal map B3 → D, where B3 is the unit 3-ball and D is a Jordan domain in R3 with boundary 2-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.},
author = {Heinonen, Juha},
journal = {Revista Matemática Iberoamericana},
keywords = {Aplicaciones cuasiconformes; Teoría de la medida; Distancia de Hausdorff; Problema de contorno; Continuidad; Simetría; quasiconformal maps; distortion theorems},
language = {eng},
number = {3},
pages = {697-725},
title = {The boundary absolute continuity of quasiconformal mappings (II).},
url = {http://eudml.org/doc/39521},
volume = {12},
year = {1996},
}

TY - JOUR
AU - Heinonen, Juha
TI - The boundary absolute continuity of quasiconformal mappings (II).
JO - Revista Matemática Iberoamericana
PY - 1996
VL - 12
IS - 3
SP - 697
EP - 725
AB - In this paper a quite complete picture is given of the absolute continuity on the boundary of a quasiconformal map B3 → D, where B3 is the unit 3-ball and D is a Jordan domain in R3 with boundary 2-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.
LA - eng
KW - Aplicaciones cuasiconformes; Teoría de la medida; Distancia de Hausdorff; Problema de contorno; Continuidad; Simetría; quasiconformal maps; distortion theorems
UR - http://eudml.org/doc/39521
ER -

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