Number of components of polynomial lemniscates: a problem of Erdös, Herzog, and Piranian

Subhajit Ghosh, Koushik Ramachandran

Let $K\subset \mathbb{C}$ be a compact set in the plane whose logarithmic capacity $c(K)$ is strictly positive. Let ${\mathcal{P}}_n(K)$ be the space of monic polynomials of degree $n…