Geodesic
Symmetrization, Green's function, and conformal mappings
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 13, Tome 226 (1996), pp. 80-92

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Let $h(z\zeta)-\log|z-\zeta|$ be the Green function of a planar domain $D$. The behavior of the linear combination $h(z,z)-h(\zeta,\zeta)-2h(z,\zeta)$ under certain symmetrization transformations of $D$ is studied. Covering and distortion theorems in the theory of univalent functions are proved as applications. Bibl. 9 titles. 
@article{ZNSL_1996_226_a7,
     author = {V. N. Dubinin},
     title = {Symmetrization, {Green's} function, and conformal mappings},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {80--92},
     publisher = {mathdoc},
     volume = {226},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1996_226_a7/}
}
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V. N. Dubinin. Symmetrization, Green's function, and conformal mappings. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 13, Tome 226 (1996), pp. 80-92. http://geodesic.mathdoc.fr/item/ZNSL_1996_226_a7/