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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {F. A. Ivlev},
     title = {Estimate of the distance between two bodies inside an $n$-dimensional unit cube and a ball},
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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/

[1] Fomenko A.T., Variational problems in topology. The geometry of length, area and volume, Gordon and Breach Science Publishers, N.Y., 1990 | MR | Zbl

[2] Dao Chong Tkhi, Fomenko A.T., Minimalnye poverkhnosti i problema Plato, Nauka, M., 1987 | MR

[3] Shiryaev A.N., Veroyatnost, MTsNMO, M., 2007 | MR