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arXiv · 2312.12603

Bounded Connected Components of Polynomial Lemniscates

Adam Kraus·Brian Simanek
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Abstract

We consider families of polynomial lemniscates in the complex plane and determine if they bound a Jordan domain. This allows us to find examples of regions for which we can calculate the projection of $\bar{z}$ to the Bergman space of the bounded region. Such knowledge has applications to the calculation of torsional rigidity.

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Adam Kraus, Brian Simanek. 2023-12-19. Bounded Connected Components of Polynomial Lemniscates. https://arxiv.org/abs/2312.12603

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