可逆齐性度量空间的拟Möbius刻画
Toward a quasi-Möbius characterization of Invertible Homogeneous Metric Spaces
摘要：
我们研究局部紧的度量空间，享有各种形式的齐性关于莫比乌斯自同胚。我们调查这种同质性和等距同质性与可逆性的结合之间的联系。特别地，我们给出了局部紧连通度量空间中非紧型秩一对称空间边界雪花的一个新刻画。此外，我们调查的一致强拟莫比乌斯自同胚的齐性度量的影响，连接这样的齐性与一致双Lipschitz齐性和拟可逆性的组合。在这种情况下，我们刻画空间包含一个切割点，并提供了几个度量性质的空间不包含割点。这些结果的动机是希望描述雪花的边界的秩一对称空间的双Lipschitz等价。
英文摘要：
We study locally compact metric spaces that enjoy various forms of homogeneity with respect to Möbius self-homeomorphisms. We investigate connections between such homogeneity and the combination of isometric homogeneity with invertibility. In particular, we provide a new characterization of snowflakes of boundaries of rank-one symmetric spaces of non-compact type among locally compact and connected metric spaces. Furthermore, we investigate the metric implications of homogeneity with respect to uniformly strongly quasi-Möbius self-homeomorphisms, connecting such homogeneity with the combination of uniform bi-Lipschitz homogeneity and quasi-invertibility. In this context we characterize spaces containing a cut point and provide several metric properties of spaces containing no cut points. These results are motivated by a desire to characterize the snowflakes of boundaries of rank-one symmetric spaces up to bi-Lipschitz equivalence.
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