Contents Online
Mathematical Research Letters
Volume 15 (2008)
Number 4
Analytic capacity and quasiconformal mappings with $W^{1,2}$ Beltrami coefficient
Pages: 779 – 793
DOI: https://dx.doi.org/10.4310/MRL.2008.v15.n4.a14
Authors
Abstract
We show that if $\phi$ is a quasiconformal mapping with compactly supported Beltrami coefficient in the Sobolev space $W^{1,2}$, then $\phi$ 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 $W^{1,2}$.
Published 1 January 2008