# Universally optimal distribution of points on spheres

@article{Cohn2006UniversallyOD, title={Universally optimal distribution of points on spheres}, author={Henry Cohn and Abhinav Kumar}, journal={arXiv: Metric Geometry}, year={2006} }

We study configurations of points on the unit sphere that minimize potential energy for a broad class of potential functions (viewed as functions of the squared Euclidean distance between points). Call a configuration sharp if there are m distances between distinct points in it and it is a spherical (2m-1)-design. We prove that every sharp configuration minimizes potential energy for all completely monotonic potential functions. Examples include the minimal vectors of the E_8 and Leech lattices…

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