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arXiv · 1807.08689

A $1$-point Quadrature domain of order $1$ not biholomorphic to a balanced domain

Pranav Haridas·Jaikrishnan Janardhanan
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Abstract

It is known that if $f: D_1 \to D_2$ is a polynomial biholomorphism with polynomial inverse and constant Jacobian then $D_1$ is a $1$-point Quadrature domain (the Bergman span contains all holomorphic polynomials) of order $1$ whenever $D_2$ is a balanced domain. Bell conjectured that all $1$-point Quadrature domains arise in this manner. In this note, we construct a $1$-point Quadrature domain of order $1$ that is not biholomorphic to any balanced domain.

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Pranav Haridas, Jaikrishnan Janardhanan. 2018-07-23. A $1$-point Quadrature domain of order $1$ not biholomorphic to a balanced domain. https://arxiv.org/abs/1807.08689

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