On the moduli space of the standard Cantor set

Abstract

We consider a generalized Cantor set $E(\omega)$ for an infinite sequence $\omega=(q_n)_{n=1}^{\infty}$ of positive numbers with $0<q_n<1$, and examine the quasiconformal equivalence to the standard middle one-third Cantor set $E(\omega_0)$. We may give a necessary and sufficient condition for $E(\omega)$ to be quasiconformally equivalent to $E(\omega_0)$ in terms of $\omega$.