Journal of Mathematical Sciences

, Volume 89, Issue 1, pp 967–975 | Cite as

Symmetrization, Green's function, and conformal mappings

  • V. N. Dubinin


Let h(zξ)−log|z−ξ| be the Green function of a planar domain D. The behavior of the linear combination h(z,z)+h(ξ,ξ)−2h(z,ξ) under certain symmetrization transformations of D is studied. Covering and distortion theorems in the theory of univalent functions are proved as applications. Bibliography: 9 titles.


Linear Combination Green Function Univalent Function Conformal Mapping Planar Domain 
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© Plenum Publishing Corporation 1998

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  • V. N. Dubinin

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