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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A method of symmetrization and applications


Author: W. E. Kirwan
Journal: Trans. Amer. Math. Soc. 163 (1972), 369-377
MSC: Primary 30A26
DOI: https://doi.org/10.1090/S0002-9947-1972-0291423-X
MathSciNet review: 0291423
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Abstract: In this paper we define a method of symmetrization for plane domains that includes as special cases methods of symmetrization considered by Szegö and by Marcus. We prove that under this method of symmetrization the mapping radius of a fixed point is not decreased. This fact is used to obtain some results concerning covering properties of Bieberbach-Eilenberg functions.


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DOI: https://doi.org/10.1090/S0002-9947-1972-0291423-X
Keywords: Conformal mapping, mapping radius, symmetrization, Univalent functions, Bieberbach-Eilenberg functions
Article copyright: © Copyright 1972 American Mathematical Society