Estimates of the Kobayashi and quasi-hyperbolic distances

TL;DR

This paper establishes universal upper bounds for the Kobayashi and quasi-hyperbolic distances near Dini-smooth boundary points in complex and real domains, enhancing understanding of their geometric properties.

Contribution

It provides the first universal upper bounds for these distances near Dini-smooth boundary points in both complex and real domains.

Findings

Universal upper bounds for Kobayashi distance near Dini-smooth boundaries

Universal upper bounds for quasi-hyperbolic distance near Dini-smooth boundaries

Improved geometric understanding of boundary behavior in complex and real domains

Abstract

Universal upper bounds for the Kobayashi and quasi-hyperbolic distances near Dini-smooth boundary points of domains in $\C^n$ and $\R^n,$ respectively, are obtained.