Sharpness of connectivity bounds for quadrature domains

preprint2014arXivOpen access

In this paper we prove the sharpness of connectivity bounds established in [15]. The proof depends on some facts in the theory of univalent polynomials. We also discuss applications to the equation $r(z)=\bar z$ where $r$ is a rational function.

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Sharpness of connectivity bounds for quadrature domains

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