Log-optimal Configurations on the Sphere
نویسندگان
چکیده
In this article we consider the distribution of N points on the unit sphere S in R interacting via logarithmic potential. A characterization theorem of the stationary configurations is derived when N = d + 2 and two new log-optimal configurations minimizing the logarithmic energy are obtained for six points on S and seven points on S. A conjecture on the log-optimal configurations of d + 2 points on S is stated and three auxiliary results supporting the conjecture are presented.
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