Abstract
One of the long-standing problems in the quasiconformal theory is finding sharp distortion bounds for k-quasiconformal maps for arbitrary \(k <1\). We provide a general distortion theorem for univalent functions in arbitrary quasiconformal disks with k-quasiconformal extensions to \(\mathbb {C}\) giving a universal power bound. Generically, this power cannot be strengthened.
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