Hyperbolic curvature of holomorphic level curves

Mihai Iancu, Veronica-Oana Nechita

We give sharp bounds for the hyperbolic curvature of the level curve $|z|=|f(z)|$, when $f:\mathbb{D}\to \mathbb{D}$ is holomorphic on the unit disc $\mathbb{D}$ and $f(0)\ne 0$, as…