The Gehring-Hayman type theorem on pseudoconvex domains of finite type in $\mathbb{C}^2$

Abstract

In this paper, we obtain the Gehring-Hayman type theorem on smoothly bounded pseudoconvex domains of finite type in $\mathbb{C}^2$. As an application, we provide a quantitative comparison between global and local Kobayashi distances near a boundary point for these domains.