A condition of quasiconformal extendability (Q1302088)

The authors investigate conditions for a quasiconformal map to be extended. They define some closed set \(E\) in the complex plane \(\mathbb{C}\) which is said to be annularly coarse and prove the following theorem: Suppose that \(f\) is a quasiconformal map of the complement of an annularly coarse set \(E\) into \(\mathbb{C}\). Then \(f\) has a quasiconformal extension to \(\widehat\mathbb{C}\). Moreover, the dilation of the extension agrees with the dilatation of \(f\).