Non-algebraic quadrature domains

Details Non-algebraic quadrature domains Non-algebraic quadrature domains

2012-02-22

arxiv.org/abs/1202.5013v1

Mathematics

Complex Variables

23 pages, 4 figures

Scientific paper

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.

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