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Sums of distances between points on a sphere


Author: Kenneth B. Stolarsky
Journal: Proc. Amer. Math. Soc. 35 (1972), 547-549
MSC: Primary 52A40
DOI: https://doi.org/10.1090/S0002-9939-1972-0303418-3
MathSciNet review: 0303418
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Abstract: An upper bound for the sum of the $ \lambda $th powers of all distances determined by N points on a unit sphere is given for $ 0 \leqq \lambda \leqq 1$.


References [Enhancements On Off] (What's this?)

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  • [2] R. Alexander and K. B. Stolarsky, Some extremal problems of distance geometry (in preparation).
  • [3] G. Björck, Distributions of positive mass which maximize a certain generalized energy integral, Ark. Mat. 3 (1955), 255-269. MR 17, 1198. MR 0078470 (17:1198b)
  • [4] L. Fejes Tóth, On the sum of distances determined by a pointset, Acta Math. Acad. Sci. Hungar. 7 (1956), 397-401. MR 21 #5937. MR 0107212 (21:5937)
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  • [6] I. J. Schoenberg, On certain metric spaces arising from Euclidean spaces by change of metric and their imbedding in Hilbert space, Ann. of Math. 38 (1937), 787-793. MR 1503370
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DOI: https://doi.org/10.1090/S0002-9939-1972-0303418-3
Article copyright: © Copyright 1972 American Mathematical Society

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