d维对数最优（d+2）-构型
Log-optimal (d+2)-configurations in d-dimensions
摘要：
我们列举并分类了d维单位球面（d-1）上d+2点的所有平稳对数构形。特别是，我们表明，对数能量达到其相对最小值的配置，包括两个正交到对方的基数m和n的正则单形。如果d是偶数，则当m=n时出现全局极小值，否则m=n+1。这刻画了一类新的构型，对于所有d，它们使（d-1）球上的对数能量最小。在文献中已知的其他两类，正规单纯形和交叉多面体，都是普遍最优配置。
英文摘要：
We enumerate and classify all stationary logarithmic configurations of d+2 points on the unit (d-1)-sphere in d-dimensions. In particular, we show that the logarithmic energy attains its relative minima at configurations that consist of two orthogonal to each other regular simplexes of cardinality m and n. The global minimum occurs when m=n if d is even and m=n+1 otherwise. This characterizes a new class of configurations that minimize the logarithmic energy on the (d-1)-sphere for all d. The other two classes known in the literature, the regular simplex and the cross polytope, are both universally optimal configurations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
