On the Uniqueness Problem for Quadrature Domains

We study questions of existence and uniqueness of quadrature domains using computational tools from real algebraic geometry. These problems are transformed into questions about the number of solutions to an associated real semi-algebraic system, which is analyzed using the method of real comprehensi...

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Bibliographic Details
Published in:	Computational methods and function theory Vol. 21; no. 3; pp. 473 - 504
Main Authors:	Ameur, Yacin, Helmer, Martin, Tellander, Felix
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01-09-2021 Springer Nature B.V
Subjects:	Algebra Analysis Computational Mathematics and Numerical Analysis Conformal mapping Domains Functions of a Complex Variable Matematik Mathematics Mathematics and Statistics Natural Sciences Naturvetenskap Quadrature domain Quadratures Questions Real comprehensive triangular decomposition Software Uniqueness 30C20 68W30 31A25 Conformal mapping 14P10 Real comprehensive triangular decomposition Quadrature domain
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Summary:	We study questions of existence and uniqueness of quadrature domains using computational tools from real algebraic geometry. These problems are transformed into questions about the number of solutions to an associated real semi-algebraic system, which is analyzed using the method of real comprehensive triangular decomposition.
ISSN:	1617-9447 2195-3724
DOI:	10.1007/s40315-021-00373-w