Quadrature domains packing
Spectral Theory
2024-11-22 v1 Complex Variables
Abstract
Given a finite family of compact subsets of the complex plane we propose a certificate of mutual non-overlapping with respect to area measure. The criterion is stated as a couple of positivity conditions imposed on a four argument analytic/anti-analytic kernel defined in a neighborhood of infinity. In case the compact sets are closures of quadrature domains the respective kernel is rational, enabling an effective matrix analysis algorithm for the non-overlapping decision. The simplest situation of two disks is presented in detail from a matrix model perspective as well as from a Riemann surface potential theoretic interpretation.
Cite
@article{arxiv.2411.14124,
title = {Quadrature domains packing},
author = {Bjorn Gustafsson and Mihai Putinar},
journal= {arXiv preprint arXiv:2411.14124},
year = {2024}
}