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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An extremal problem for quasiconformal mappings in an annulus
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by Alvin M. White PDF
Proc. Amer. Math. Soc. 71 (1978), 267-274 Request permission


The following extremal problem is solved. We consider a family of continuously differentiable univalent quasiconformal mappings $w = f(z)$ of the annulus $r < |z| < 1$ onto the unit disk minus some continuum containing the origin. For a point b on a fixed circle, maximize $|f(b)|$ within the family. The problem is solved by using a variational method due to Schiffer. The extremal function and the maximum are found in terms of the Weierstrass $\wp$-function and the elliptic modular function.
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 71 (1978), 267-274
  • MSC: Primary 30A38; Secondary 30A60
  • DOI:
  • MathSciNet review: 0480981