On Fridman invariant, injectivity radius function and squeezing function

TL;DR

This paper explores the relationship between the Fridman invariant, injectivity radius, and squeezing function in certain domains, providing explicit formulas and analyzing their properties within complex analysis.

Contribution

It identifies classes of domains where the Fridman invariant and injectivity radius coincide under the Carathéodory metric and derives explicit squeezing function expressions.

Findings

Fridman invariant and injectivity radius coincide in specific domains.

Explicit formulas for squeezing functions are obtained.

Properties of these functions are analyzed in the given domains.

Abstract

We give a class of domains for which Fridman invariant and injectivity radius function coincide with respect to Carath\'eodory metric. We give explicit expressions of the squeezing functions for these domains and investigate some of their properties.