Topology of quadrature domains

TL;DR

This paper investigates the topological properties of quadrature domains, establishing upper bounds on their connectivity based on the number and multiplicities of nodes in the quadrature identity.

Contribution

It provides new bounds on the connectivity of quadrature domains relating to the nodes and their multiplicities, advancing understanding of their topological structure.

Findings

Derived upper bounds on domain connectivity

Linked topology to nodes and multiplicities

Enhanced theoretical understanding of quadrature domains

Abstract

We address the problem of topology of quadrature domains, namely we give upper bounds on the connectivity of the domain in terms of the number of nodes and their multiplicities in the quadrature identity.