MESH RATIOS FOR BEST-PACKING AND LIMITS OF MINIMAL ENERGY CONFIGURATIONS

作者：Bondarenko A V; Hardin D P; Saff E B^*

来源：Acta Mathematica Hungarica, 2014, 142(1): 118-131.

DOI：10.1007/s10474-013-0339-3

• best-packing
• mesh norm
• separation distance
• quasi-uniformity
• Riesz energy
• covering constant

For N-point best-packing configurations omega (N) on a compact metric space (A,rho), we obtain estimates for the mesh-separation ratio gamma(omega (N) ,A), which is the quotient of the covering radius of omega (N) relative to A and the minimum pairwise distance between points in omega (N) . For best-packing configurations omega (N) that arise as limits of minimal Riesz s-energy configurations as s -> a, we prove that gamma(omega (N) ,A)a parts per thousand broken vertical bar 1 and this bound can be attained even for the sphere. In the particular case when N=5 on S (2) with rho 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 , that is the limit (as s -> a) of 5-point s-energy minimizing configurations. Moreover, .

• 出版日期2014-2