Analytic capacity and quasiconformal mappings with $W^{1,2}$ Beltrami coefficient

Albert Clop, Xavier Tolsa
2008 Mathematical Research Letters  
We show that if φ is a quasiconformal mapping with compactly supported Beltrami coefficient in the Sobolev space W 1,2 , 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 W 1,2 .
doi:10.4310/mrl.2008.v15.n4.a14 fatcat:z7bkhiq3rfhdrnrwfrhqn7nsy4