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math.MG2026
The Uniform Gromov Hausdorff Gap Problem for Approximating Spheres by Finite Homogeneous Spaces
Itai Benjamini
Let be the unit round sphere with its intrinsic angular metric, normalized so that . For finite homogeneous metric spaces , put \[ δ_n=\inf_X d…
math.MG2026
Euclidean vs Graph Metric: The Fixed-Source Problem
Itai Benjamini
We prove that two fixed sources in the Euclidean plane can be realized by a bounded-degree planar unit-edge graph on a 10-net, with graph distance from each source agreeing with Eu…
math.MG2026
Determining a Points Configuration from a Subset of the Pairwise Distances
Itai Benjamini, Elad Tzalik
We study rigidity without assuming general position. Given distinct labelled points and a set of revealed pairs, we ask when the correspon…