## Quasiconformal mappings and sets of finite perimeter

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- by James C. Kelly
- Trans. Amer. Math. Soc.
**180**(1973), 367-387 - DOI: https://doi.org/10.1090/S0002-9947-1973-0357783-7
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## Abstract:

Let $D$ be a domain in ${R^n},n \geqslant 2,f$ a quasiconformal mapping on $D$. We give a definition of*bounding surface of codimension one lying in*$D$, and show that, given a system $\Sigma$ of such surfaces, the image of the restriction of $f$ to “almost every” surface is again a surface. Moreover, on these surfaces, $f$ takes ${H^{n - 1}}$ (Hausdorff $(n - 1)$-dimensional) null sets to ${H^{n - 1}}$ null sets. “Almost every” surface is given a precise meaning via the concept of the module of a system of measures, a generalization of the concept of extremal length.

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## Bibliographic Information

- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**180**(1973), 367-387 - MSC: Primary 30A60; Secondary 28A75
- DOI: https://doi.org/10.1090/S0002-9947-1973-0357783-7
- MathSciNet review: 0357783