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Asymptotic properties of unbounded quadrature domains the plane. (English) Zbl 1383.30002

Summary: We prove that if \(\Omega\) is a simply connected quadrature domain (QD) of a distribution with compact support and the point of infinity belongs to the boundary, then the boundary has an asymptotic curve that is a straight line, parabola or infinite ray. In other words, such QDs in the plane are perturbations of null QDs.

MSC:

30C20 Conformal mappings of special domains
30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
35R35 Free boundary problems for PDEs
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