Abstract:
The problem of estimation of the distance between two bodies of volume $\varepsilon$ located inside an $n$-dimensional body $B$ of unit volume where $n \to \infty$ is considered. In some cases such distances are bounded by a function of $\varepsilon$ not dependent on $n$. The cases when $B$ is a sphere or a cube are considered.
Key words:minimal surface, multidimensional convex geometry, central limit theorems.
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