Geodesic
Estimate of the distance between two bodies inside an $n$-dimensional unit cube and a ball
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2015), pp. 23-28

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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. 
@article{VMUMM_2015_6_a3,
     author = {F. A. Ivlev},
     title = {Estimate of the distance between two bodies inside an $n$-dimensional unit cube and a ball},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {23--28},
     publisher = {mathdoc},
     number = {6},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2015_6_a3/}
}
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F. A. Ivlev. Estimate of the distance between two bodies inside an $n$-dimensional unit cube and a ball. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2015), pp. 23-28. http://geodesic.mathdoc.fr/item/VMUMM_2015_6_a3/