Geodesic
On the change in harmonic measure under symmetrization
Sbornik. Mathematics, Tome 52 (1985) no. 1, pp. 267-273 
V. N. Dubinin. On the change in harmonic measure under symmetrization. Sbornik. Mathematics, Tome 52 (1985) no. 1, pp. 267-273. http://geodesic.mathdoc.fr/item/SM_1985_52_1_a14/
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     author = {V. N. Dubinin},
     title = {On the change in harmonic measure under symmetrization},
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     year = {1985},
     volume = {52},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1985_52_1_a14/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $D_\alpha$ be the unit disc cut along the segments $l_k=\{z:\arg z=\alpha_k,\ r\leqslant|z|\leqslant1\}$, $k=0,1,\dots,n-1$ ($\alpha=(\alpha_0,\alpha_1,\dots,\alpha_{n-1})$, $0), and let $\omega_\alpha$ be the harmonic measure of the set $\bigcup\limits_{k=0}^{n-1}l_k$ relative to the region $D_\alpha$ at the point $z=0$. An affirmative solution is given of a problem of A. A. Gonchar: $$ \omega_\alpha\leqslant\omega_{\alpha^*} $$ where $\alpha^*=\bigl(0,\frac{2\pi}n,\dots,\frac{2\pi}n(n-1)\bigr)$. Equality holds only when $D_\alpha$ coincides with $D_{\alpha^*}$ to within a rotation about the origin. The proof is based on a property of certain condensers under dissymmetrization, i.e. under a transformation of symmetric condensers into nonsymmetric ones. Bibliography: 4 titles.

[1] Tamrazov P. M., “Emkosti kondensatorov. Metod peremeshivaniya zaryadov”, Matem. sb., 115(157) (1981), 40–73 | MR | Zbl

[2] Stoilov S., Teoriya funktsii kompleksnogo peremennogo, T. 2, IL, M., 1962

[3] Kheiman V. K., Mnogolistnye funktsii, IL, M., 1960

[4] Dzhenkins Dzh., Odnolistnye funktsii i konformnye otobrazheniya, IL, M., 1962