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

TL;DR

This paper establishes a Gehring-Hayman type theorem for smoothly bounded pseudoconvex domains of finite type in rac{}2, providing insights into the relationship between global and local Kobayashi distances near boundary points.

Contribution

It extends the Gehring-Hayman theorem to a new class of complex domains and offers a quantitative comparison of Kobayashi distances near boundary points.

Findings

Proved a Gehring-Hayman type theorem for pseudoconvex domains of finite type in rac{}2.

Established a quantitative relationship between global and local Kobayashi distances.

Enhanced understanding of boundary behavior in complex analysis.

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.