A stable configuration of 102 points on the sphere. The sphere has been partitioned into Voronoi cells associated to each point, which have been colored by the number of neighbors.

Discrete Minimal Energy Problems

Configurations of points on the two-sphere that minimize the pairwise electrostatic energy have been the focus of considerable investigation. Computational efforts to find such energy-minimizing configurations are hampered by the presence of many locally minimal but not glob-ally minimal, i.e. stable, configurations. This work aims to answer the question: how many stable configurations are there?

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