6 papers · 1 filter
Gromov-Hausdorff distance between chromatic metric pairs and stability of the six-pack
Ondřej Draganov, Sophie Rosenmeier, Nicolò Zava
Chromatic metric pairs consist of a metric space and a coloring function partitioning a subset thereof into various colors. It is a natural extension of the notion of chromatic poi…
Topological dimension of the Gromov-Hausdorff and Gromov-Prokhorov spaces
Hiroki Nakajima, Takamitsu Yamauchi, Nicolò Zava
The Gromov-Hausdorff distance is a dissimilarity metric capturing how far two spaces are from being isometric. The Gromov-Prokhorov distance is a similar notion for metric measure…
Lower Bounding the Gromov--Hausdorff distance in Metric Graphs
Henry Adams, Sushovan Majhi, Fedor Manin +2
Let be a finite, connected metric graph and let be a subset. If is sufficiently dense in , we show that the Gromov--Hausdorff distance matches the Hausdor…
Coarse structures on locally compact abelian groups
Dmitri Shakhmatov, Takamitsu Yamauchi, Nicolò Zava
Motivated by the study of the large-scale geometry of topological groups, we investigate particular families of subsets of topological groups named group ideals. We compare differe…
On the metric spaces of lattices and periodic point sets
Alexey Garber, Žiga Virk, Nicolò Zava
Lattices and periodic point sets are well known objects from discrete geometry. They are also used in crystallography as one of the models of atomic structure of periodic crystals.…
Coarse and bi-Lipschitz embeddability of subspaces of the Gromov-Hausdorff space into Hilbert spaces
Nicolò Zava
In this paper, we discuss the embeddability of subspaces of the Gromov-Hausdorff space, which consists of isometry classes of compact metric spaces endowed with the Gromov-Hausdorf…