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The lower bound of the maximal dilatation of the Beurling-Ahlfors extension. (English) Zbl 0723.30016

The author gives an example of a piecewise linear \(\rho\)-quasisymmetric function \((\rho >1)\) such that the corresponding Beurling-Ahlfors extension to the upper halfplane has maximal dilatation \(\geq (2\rho +1)(1-1\sqrt{\rho})\). The result shows that an estimate from above given by Lehtinen is asymptotically sharp as \(\rho\to \infty\).

MSC:

30C62 Quasiconformal mappings in the complex plane
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