Non-algebraic quadrature domains
Complex Variables
2013-10-29 v1
Abstract
It is well known that, in the plane, the boundary of any quadrature domain (in the classical sense) coincides with the zero set of a polynomial. We show, by explicitly constructing some four-dimensional examples, that this is not always the case. This confirms, in dimension 4, a conjecture of the second author. Our method is based on the Schwarz potential and involves elliptic integrals of the third kind.
Cite
@article{arxiv.1202.5013,
title = {Non-algebraic quadrature domains},
author = {Alexandre Eremenko and Erik Lundberg},
journal= {arXiv preprint arXiv:1202.5013},
year = {2013}
}
Comments
23 pages, 4 figures