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- W2065640907 abstract "For N-point best-packing configurations ω N on a compact metric space (A,ρ), we obtain estimates for the mesh-separation ratio γ(ω N ,A), which is the quotient of the covering radius of ω N relative to A and the minimum pairwise distance between points in ω N . For best-packing configurations ω N that arise as limits of minimal Riesz s-energy configurations as s→∞, we prove that γ(ω N ,A)≦1 and this bound can be attained even for the sphere. In the particular case when N=5 on S 2 with ρ the Euclidean metric, we prove our main result that among the infinitely many 5-point best-packing configurations there is a unique configuration, namely a square-base pyramid $omega_{5}^{*}$ , that is the limit (as s→∞) of 5-point s-energy minimizing configurations. Moreover, $gamma(omega_{5}^{*},S^{2})=1$ ." @default.
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- W2065640907 date "2013-08-02" @default.
- W2065640907 modified "2023-10-18" @default.
- W2065640907 title "Mesh ratios for best-packing and limits of minimal energy configurations" @default.
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- W2065640907 doi "https://doi.org/10.1007/s10474-013-0339-3" @default.
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