Calculus of Variations and Geometric Measure Theory
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Z. Balogh - P. Koskela - S. Rogovin

Absolute continuity continuity of quasiconformal mappings on curves

created by zoltan on 08 Dec 2004
modified on 13 Aug 2007

[BibTeX]

Accepted Paper

Inserted: 8 dec 2004
Last Updated: 13 aug 2007

Journal: GAFA
Year: 2007

Abstract:

We show that a quasiconformal mapping between two proper, locally $Q$-regular metric spaces $Q>1$, is absolutely continuous on almost every curve. We further relax the limes superior in the definition of quasiconformality to limes inferior and verify that exceptional sets analogous to the Euclidean setting can be allowed.

Keywords: absolute continuity, quasiconformal mappings, Sobolev space


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