Examples of fractals satisfying the quasihyperbolic boundary condition

TL;DR

This paper provides explicit examples of bounded domains satisfying the quasihyperbolic boundary condition, calculates the associated constants, and explores their properties as John domains, filling a gap in existing literature.

Contribution

It introduces explicit domain examples with calculated quasihyperbolic and John constants, providing precise parameter estimates not previously documented.

Findings

Explicit examples of domains satisfying the quasihyperbolic boundary condition

Calculated exact values of quasihyperbolic and John constants

First known estimates of these parameters in such domains

Abstract

In this paper we give explicit examples of bounded domains that satisfy the quasihyperbolic boundary condition and calculate the values for the constants. These domains are also John domains and we calculate John constants as well. The authors do not know any other paper where exact values of parameters has been estimated.