Disposition points on a sphere with minimum of energy. (English. Russian original) Zbl 0929.52010

Andreev, N. N.

Proc. Steklov Inst. Math. 219, 20-24 (1997); translation from Tr. Mat. Inst. Steklova 219, 27-31 (1997).

The author considers the disposition of \(N\) points on the unit sphere \[ S^{d-1} =\bigl\{(x_1, x_2,\dots, x_d)\in \mathbb{R}^d/x^2_1 +x_2^2+ \cdots x^2_d= 1\bigr\} \] in the \(d\)-dimensional Euclidean space which minimizes the energy functional. He shows that for \(d=24\) and \(N=196 560\) the extremal construction is defined by the minimal vectors of the Leech lattice and gives the exact values of the energy functionals.
For the entire collection see [Zbl 0907.00017].

MSC:

52C10

Erdős problems and related topics of discrete geometry

Keywords:

disposition points; minimum of energy; unit sphere