A Counterexample to a Problem of Pommerenke on Convex Functions in the Class $\Sigma$

Yuankai Guo, Xiaozhe Hu

Let $\Sigma$ denote the class of functions $f(z)=z+b_0+b_1{z}^{-1}+\cdots$ that are analytic and univalent in the exterior unit disk ${\Delta }^{\ast }=\{z\in \mathbb{C}:|z|>1\}$. In 19…