Boundary behavior of the quasi-hyperbolic metric

TL;DR

This paper investigates how the quasi-hyperbolic metric behaves near smooth boundary regions of a domain in Euclidean space, providing precise characterizations of its boundary behavior.

Contribution

It offers a detailed analysis of the boundary behavior of the quasi-hyperbolic metric in domains with smooth boundaries, advancing understanding in geometric function theory.

Findings

Precise boundary behavior characterization of the quasi-hyperbolic metric.

Results applicable to domains with $ ext{C}^{1,1}$-smooth boundaries.

Enhanced understanding of geometric properties near boundary regions.

Abstract

The precise behavior of the quasi-hyperbolic metric near a $\mathcal C^{1,1}$-smooth part of the boundary of a domain in $\mathbb{R}^n$ is obtained.