Abstract
The problem of estimation of the distance between two bodies of volume ε located inside an n-dimensional body B of unit volume is considered in the case n→∞. In some cases such distances are bounded by a function of ε not dependent on n. The cases when B is a sphere or a cube are considered.
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References
A. T. Fomenko, Variational Problems in Topology. The Geometry of Length, Area and Volume (Gordon and Breach Sei. Publ., N.Y., 1990).
A. T. Fomenko and Dao Chong Thi, Minimal Surfaces and Plateau Problem (Nauka, Moscow, 1987; American Math. Soc., 1991).
A. N. Shiryaev, Probability (MCCME, Moscow, 2007) [in Russian]
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Original Russian Text © F.A. Ivlev, 2015, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2015, Vol. 70, No. 6, pp. 23–28.
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Ivlev, F.A. Estimate of the distance between two bodies inside an n-dimensional unit cube and a ball. Moscow Univ. Math. Bull. 70, 261–266 (2015). https://doi.org/10.3103/S0027132215060042
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DOI: https://doi.org/10.3103/S0027132215060042