Bounded Connected Components of Polynomial Lemniscates

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.

Significant change to Lemma 2.1 and the way it was applied