On an isoperimetric problem in conformal mapping

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.

Keywords:

• Szegö
• kernel
• N-widths
• Hilbert matrix
• Doubly orthogonal functions

Keywords:

• 19991 Mathematics Subject Classifications:
• 30C30
• 30C35

Notes

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