By introducing new deformations on symbolic Cantor sets and ultrametric spaces, we prove that doubling ultrametric spaces admit bilipschitz embedding into Cantor sets. If in addition the spaces are uniformly perfect, we show that they are quasisymmetrically equivalent to Cantor sets. Moreover, we provide a new proof for a recent work of Heer regarding quasimöbius uniformization of Cantor set.

中文翻译：

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符号Cantor集和超空间上的变形

通过在符号Cantor集和超度量空间上引入新的变形，我们证明加倍的超度量空间允许bilipschitz嵌入Cantor集。此外，如果空间是一致理想的，则表明它们与Cantor集准对称等效。此外，我们为Heer关于Cantor集的拟似比均匀化的最新工作提供了新的证据。