Sharpness of connectivity bounds for quadrature domains

Abstract

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.

arXiv comment35 pages, 11 figures

References in corpus (2)

• Topology of quadrature domains
• n-point Gravitational Lenses with 5(n-1) Images

Cited by in corpus (3)

• Topology of quadrature domains
• Circle packings, kissing reflection groups and critically fixed anti-rational maps
• Univalent Polynomials and Hubbard Trees