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Journal of Mathematical Sciences

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

Symmetrization, Green's function, and conformal mappings

  • V. N. Dubinin
Article

Abstract

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.

Keywords

Linear Combination Green Function Univalent Function Conformal Mapping Planar Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • V. N. Dubinin

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