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Asymptotic properties of unbounded quadrature domains the plane

Published online by Cambridge University Press:  07 January 2015

LAVI KARP
LAVI KARP*
Affiliation:
Department of Mathematics, ORT Braude College, P.O. Box 78, 21982 Karmiel, Israel email: karp@braude.ac.il
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Abstract

We prove that if Ω 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.

Keywords

quadrature domainsasymptotic curveCauchy transformcontact surfacesnull quadrature domainsconformal mappingfree boundaries
Type
Papers
Information
European Journal of Applied Mathematics , Volume 26 , Issue 2 , April 2015 , pp. 175 - 191
Copyright
Copyright © Cambridge University Press 2015 

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