Geodesic
Polarization and circular truncation of a~domain
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 30, Tome 440 (2015), pp. 162-169

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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 $D\cap\{\left|z\right|$, 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. 
@article{ZNSL_2015_440_a10,
     author = {V. O. Kuznetsov},
     title = {Polarization and circular truncation of a~domain},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {162--169},
     publisher = {mathdoc},
     volume = {440},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_440_a10/}
}
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V. O. Kuznetsov. Polarization and circular truncation of a~domain. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 30, Tome 440 (2015), pp. 162-169. http://geodesic.mathdoc.fr/item/ZNSL_2015_440_a10/