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Absolute Continuity of Quasiconformal Mappings on Curves

Balogh, Zoltán ; Koskela, Pekka ; Rogovin, Sari

In: GAFA Geometric And Functional Analysis, 2007, vol. 17, no. 3, p. 645-664

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    Title
    • Absolute Continuity of Quasiconformal Mappings on Curves
    Author
    • Balogh, Zoltán. Mathematisches Institut, Universität Bern, Sidlerstrasse 5, CH-3012, Bern, Switzerland
    • Koskela, Pekka. Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, FIN-40014, Jyväskylä, Finland
    • Rogovin, Sari. Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, FIN-40014, Jyväskylä, Finland
    Document Type
    • Postprint
    Language
    • English
    Published in
    • GAFA Geometric And Functional Analysis, 2007, vol. 17, no. 3, p. 645-664. Birkhäuser-Verlag; www.birkhäuser.ch
    Other Version
    OAI-PMH Identifier
    • oai:doc.rero.ch:312804
    Summary
    Abstract.: We show that a quasiconformal mapping between two proper, locally Ahlfors Q-regular metric spaces, Q > 1, is absolutely continuous on almost every curve. We further relax the limes superior in the definition of quasiconformality to a limes inferior and verify that exceptional sets analogous to the Euclidean setting can be allowed