6533b82afe1ef96bd128b6de
RESEARCH PRODUCT
Analytic capacity and quasiconformal mappings with $W^{1,2}$ Beltrami coefficient
Albert ClopXavier Tolsasubject
Sobolev spaceQuasiconformal mappingComputer Science::GraphicsCompact spaceMathematics::Complex VariablesGeneral MathematicsBounded functionMathematical analysisAnalytic capacityAnalytic functionMathematicsdescription
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 $W^{1,2}$.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2008-01-01 | Mathematical Research Letters |