Hyperbolic convexity of holomorphic level sets

Iason Efraimidis, Pavel Gumenyuk

We prove that the sublevel set $\{z\in \mathbb{D}:k_{\mathbb{D}}(z,z_0)-k_{\mathbb{D}}(f(z),w_0)<\mu \}$, $\mu \in \mathbb{R}$, is geodesically convex with resp…