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Complex Variables and Elliptic Equations
An International Journal
Volume 52, 2007 - Issue 2-3: A tribute to Peter Duren
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Original Articles

On an isoperimetric problem in conformal mapping

Yuk J. Leung Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USACorrespondence[email protected]
Pages 135-151 | Received 08 Sep 2006, Published online: 19 Oct 2007
 
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Abstract

We characterize the Jordan domain of a given perimeter L > 4 such that the two designated interior points ±1 lying in its interior have the smallest hyperbolic distance between them. We also show how this result serves as an example illustrating the theory of quadrature domains studied by Björn Gustafsson and Harold Shapiro.

†Dedicated to Professor Peter L. Duren on the occasion of his 70th birthday.

Notes

†Dedicated to Professor Peter L. Duren on the occasion of his 70th birthday.

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