A quasi-isometric analogue of the Gromov–Hausdorff distance is defined, shown to sit between GH and pointed-GH convergence, metrizable, and path-connected on quasi-isometry classes.
Hausdorff vs Gromov–Hausdorff distances
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Quasi-isometric modification of Gromov-Hausdorff distance
A quasi-isometric analogue of the Gromov–Hausdorff distance is defined, shown to sit between GH and pointed-GH convergence, metrizable, and path-connected on quasi-isometry classes.