Annales Academiĉ Scientiarum Fennicĉ
Mathematica
Volumen 32, 2007, 341-352

A REMARK ON QUASICONFORMAL DIMENSION DISTORTION ON THE LINE

István Prause

University of Helsinki, Department of Mathematics and Statistics
P.O. Box 68, FI-00014 University of Helsinki; istvan.prause 'at' helsinki.fi

Abstract. The general dimension distortion result of Astala says that a one dimensional set goes to a set of dimension at least 1 - k under a k-quasiconformal mapping. An improved version for rectifiable sets appears in recent work of Astala, Clop, Mateu, Orobitg and Uriarte-Tuero in connection with quasiregular removability problems. We give an alternative proof of their result establishing a bound of the form 1 - ck², provided that either the initial or the target set lies on a straight line. The bound 1 - k² holds under the additional assumption that the line stays fixed.

2000 Mathematics Subject Classification: Primary 30C62.

Key words: Quasiconformal mappings, dimension distortion.

Reference to this article: I. Prause: A remark on quasiconformal dimension distortion on the line. Ann. Acad. Sci. Fenn. Math. 32 (2007), 341-352.

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