1
vote
2answers
81 views

Optimal Configuration for a Set of Points

Consider a set of $n$ points on the plane with positions $\mathbf{p}_1,\dots,\mathbf{p}_n$, such that each point $i$ has at least one neighbor $j$ at a distance of no more than $\lambda$ away from it ...
2
votes
1answer
196 views

Maximal mapping of a convex set to the unit disk

EDIT: To make my question more precise i think we can narrow it down to this. Say you have a simple polygon that includes the origin, that is completely contained in the unit disk, we can 'blow up' ...
10
votes
2answers
553 views

If the Minkowski sum of two convex closed sets is a Euclidean ball, then can the two sets be anything other than Euclidean balls?

If for two convex closed sets $S_1$ and $S_2$, the Minkowski sum is a Euclidean ball then can $S_1$ and $S_2$ be anything other than Euclidean balls themselves. I suspect they can be but I haven't ...