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Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
4
votes
closest equidistant point to N points in M dimensions
If such a point exists, then it is the center of a sphere on which all $N$ points lie, so I think your question is equivalent to asking, do all $N$ points lie on some sphere? Since $M+1$ points deter …
1
vote
Diameter of random segment intersection graph?
I don't have sufficient privileges to add a comment, but I wanted to ask if your evidence is consistent with the conclusion that the diameter of $G$ increases logarithmically with $n$. That would hav …
1
vote
Blowing up spheres in a face centered cubic (fcc) packing geometry just enough to cover the ...
Although not directly answering the question, the discussion here highlights connections between the question of $R_v$ and the Voronoi cell of this lattice. In short, it turns out that $R_v$ is the m …