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
DOI:
https://doi.org/10.1090/S0002-9939-1993-1161400-4
MathSciNet review:
1161400
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Abstract | References | Similar Articles | Additional Information
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:
https://doi.org/10.1090/S0002-9939-1993-1161400-4
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