Quasisymmetric extension, smoothing and applications

Abstract

We discuss quasisymmetric extension of embeddings that are close to similarities, due to Tukia and Väisälä, and smooth quasiconformal approximation of such extensions. The smoothing is done by convolution with a variable kernel in conjunction with the Tukia-Väisälä extension procedure. We can apply these to the study of branch sets of smooth quasiregular maps, and quasiconformal dimension of self-similar fractals.