JournalsrmiVol. 37, No. 2pp. 671–722

Toward a quasi-Möbius characterization of invertible homogeneous metric spaces

  • David Freeman

    University of Cincinnati Blue Ash College, USA
  • Enrico Le Donne

    Università di Pisa, Italy, and University of Jyväskylä, Finland
Toward a quasi-Möbius characterization of invertible homogeneous metric spaces cover

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Abstract

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.

Cite this article

David Freeman, Enrico Le Donne, Toward a quasi-Möbius characterization of invertible homogeneous metric spaces. Rev. Mat. Iberoam. 37 (2020), no. 2, pp. 671–722

DOI 10.4171/RMI/1211