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 $\omega$.

arXiv commentI write another paper whch includes the results of this paper