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2. Scar behavior

    1.     Voronoi tessellation of a configuration with near-optimal Riesz energy on the sphere displays scars — sets of pairs of 5- and 7-gons. These sets form what appears to be a 1-dimensional submanifold of the 2-sphere.

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      Problem 2.15.

      [Florian Theil, Carlos Beltrán] Study the properties of scars. Why are scars low-dimensional? What is the asymptotic of the total length, number of cells, etc, for $N\to \infty$, where $N$ is the number of Riesz charges.

          Cite this as: AimPL: Minimal energy problems with Riesz potentials, available at http://aimpl.org/energyrieszV.