Polarization and circular truncation of a domain

Difference of the reduced module $m(D)$ of a simply connected domain $D$ with respect to $z=0$ and the reduced module $m(D_r)$ of its circular truncation, where $D_r$ is the connected component of the set $D\cap\{\left|z\right|<r\}$, containing the point $z=0$, is considered. It is proved that in the case of polarization and circular symmetrization of the domain $D$ this difference does not decrease.