Quasiconformal mappings and Ahlfors-David curves

Author:
Paul MacManus

Journal:
Trans. Amer. Math. Soc. **343** (1994), 853-881

MSC:
Primary 30C65

DOI:
https://doi.org/10.1090/S0002-9947-1994-1202420-6

MathSciNet review:
1202420

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Abstract: We show that if is a quasiconformal mapping of the plane whose dilatation satisfies a certain quadratic Carleson measure condition relative to an Ahlfors-David curve then is differentiable almost everywhere on and . When is chord-arc we show that its image is a Bishop-Jones curve. If the Carleson norm is small then we show that is absolutely continuous on , the image of is an Ahlfors-David curve, and , where with a small norm.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1994-1202420-6

Keywords:
Quasiconformal mapping,
Ahlfors-David curve,
Carleson measures,
BMO

Article copyright:
© Copyright 1994
American Mathematical Society