Sierpienski地毯在平面上的均匀化
Uniformization of Sierpiński carpets in the plane
摘要：
设$S_i$，$i\in I$是扩充复平面$\Sph$中的可数Jordan曲线集合，它们是两两不相交的Jordan闭区域的边界.若Jordan曲线是一致拟圆且一致相对分离，则存在一个拟共形映射$f\: \Sph\ra \Sph$，使得对所有$i\in I$，$f(S_i)$是一个圆.这意味着$\oC$中每一个周边圆是均匀相对分离的均匀拟圆的Sierpienski地毯都可以通过一个拟对称映射映射到一个圆形Sierpienski地毯上。
英文摘要：
Let $S_i$, $i\in I$, be a countable collection of Jordan curves in the extended complex plane $\Sph$ that bound pairwise disjoint closed Jordan regions. If the Jordan curves are uniform quasicircles and are uniformly relatively separated, then there exists a quasiconformal map $f\: \Sph\ra \Sph$ such that $f(S_i)$ is a round circle for all $i\in I$. This implies that every Sierpiński carpet in $\oC$ whose peripheral circles are uniformly relatively separated uniform quasicircles can be mapped to a round Sierpiński carpet by a quasisymmetric map.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
