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Notes on the boundaries of quadrature domains

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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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Acknowledgements

Many thanks are due to Björn Gustafsson for encouragement and helpful comments on an earlier draft of these notes.

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  1. Department of Mathematics, Indian Institute of Science, Bangalore, 560 012, India

    Kaushal Verma

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  1. Kaushal Verma
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Correspondence to Kaushal Verma.

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The author declares that he has no conflict of interest.

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The author was supported in part by a UGC–CAS Grant.

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Verma, K. Notes on the boundaries of quadrature domains. Anal.Math.Phys. 9, 617–638 (2019). https://doi.org/10.1007/s13324-018-0221-0

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