The existence of quasiconformal homeomorphism between planes with countable marked points

摘要

We consider quasiconformal deformations of $\mathbb{C}\setminus\mathbb{Z}$.We give some criteria for infinitely often punctured planes to bequasiconformally equivalent to $\mathbb{C}\setminus\mathbb{Z}$. In particular,we characterize the closed subsets of $\mathbb{R}$ whose compliments arequasiconformally equivalent to $\mathbb{C}\setminus\mathbb{Z}$.