Analytic capacity and quasiconformal mappings with W1,2 Beltrami coefficient

Abstract

We show that if φ a quasiconformal mapping with compactly supported Beltrami coefficient in the Sobolev space W1,2, then φ preserves sets with vanishing analytic capacity. It then follows that a compact set E is removable for bounded analytic functions if and only if it is removable for bounded quasiregular mappings with compactly supported Beltrami coefficient in W1,2. © International Press 2008.