Toward a quasi-Möbius characterization of invertible homogeneous metric spaces

• David Freeman ^[1] ; Enrico Le Donne ^[2]
  1. [1] University of Cincinnati

     University of Cincinnati

     City of Cincinnati, Estados Unidos

     
  2. [2] University of Pisa

     University of Pisa

     Pisa, Italia

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 37, Nº 2, 2021, págs. 671-722
• Idioma: inglés
• DOI: 10.4171/rmi/1211
• Enlaces
  • Texto completo
• Resumen

  • 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.