自仿射毯上拟对称映射的刚性
Rigidity of quasisymmetric mappings on self-affine carpets
摘要：
我们证明了水平自仿射毯之间的拟对称映射类是刚性的。这样的映射只有当地毯的维数一致时才存在，在这种情况下，拟对称映射是拟Lipschitz的。我们还表明，水平自仿射地毯是最小的共形Assouad尺寸。
英文摘要：
We show that the class of quasisymmetric maps between horizontal self-affine carpets is rigid. Such maps can only exist when the dimensions of the carpets coincide, and in this case, the quasisymmetric maps are quasi-Lipschitz. We also show that horizontal self-affine carpets are minimal for the conformal Assouad dimension.
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