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.


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
Full Text: DOI arXiv


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