Notes on the boundaries of quadrature domains

2016/12/20 by Verma, Kaushal
#32D15 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1612.06567

Abstract

We highlight an intrinsic connection between classical quadrature domains and the well-studied theme of removable singularities of analytic sets in several complex variables. Exploiting this connection provides a new framework to recover several basic properties of such domains, namely the algebraicity of their boundary, a better understanding of the associated defining polynomial and the possible boundary singularities that can occur.

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