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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A finite capacity analogue of the Koebe one-quarter theorem


Author: Robin Cunningham
Journal: Proc. Amer. Math. Soc. 119 (1993), 869-875
MSC: Primary 30C25
MathSciNet review: 1161400
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Abstract: A variational method is used to determine the largest disk about the origin covered by the image of every normalized univalent function that maps the unit disk onto a region of prescribed logarithmic capacity (transfinite diameter).


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1161400-4
PII: S 0002-9939(1993)1161400-4
Keywords: Univalent functions, maximal covered disks, extremal problems, variational methods, quadratic differentials, logarithmic capacity, transfinite diameter, elliptic integrals
Article copyright: © Copyright 1993 American Mathematical Society