Lipschitz distance between clouds

2025/10/26 by Mikhailov, Ivan N.
#51F99 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2510.22696

Abstract

In this note we show that the Lipschitz distance between the classes of metric spaces at finite Gromov-Hausdorff distances from the one-point metric space and the real line with the natural metric, respectively, is positive.

Citations

• Geodesic in the Gromov-Hausdorff class for which the real line is an interior point
• On the Gromov-Hausdorff distance between the cloud of bounded metric spaces and a cloud with nontrivial stabilizer
• Gromov-Hausdorff class: its completeness and cloud geometry

Related

• On the Gromov-Hausdorff distance between the cloud of bounded metric spaces and a cloud with nontrivial stabilizer
• Lipschitz (non-)equivalence of the Gromov--Hausdorff distances, including on ultrametric spaces
• The distance function and Lipschitz classes of mappings between metric spaces
• Ultrametric spaces and clouds
• Another introduction to the geometry of metric spaces