Symmetrization, Green's function, and conformal mappings

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.