Estimate of the Distance Between Two Bodies Inside an n-Dimensional Unit Cube and a Ball / F. A. Ivlev. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2015. № 6. P. 23-28 [Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 261-266].

The problem of estimation of the distance between two bodies of volume \varepsilon located inside an n-dimensional body B of unit volume is considered in the case n \to \infty . 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.