Calculus of Variations and Geometric Measure Theory

E. Le Donne - D. Freeman

Toward a quasi-Möbius characterization of Invertible Homogeneous Metric Spaces

created by ledonne on 20 Dec 2018


Submitted Paper

Inserted: 20 dec 2018
Last Updated: 20 dec 2018

Year: 2018

ArXiv: 1812.03313 PDF


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.

Tags: GeoMeG