球面上的控制与极小能量
Majorization and minimal energy on spheres
摘要：
本文研究单位球面上$m$ -点组态的f-能势的优控制定理（也称为Karamata不等式）和优控制的极小值（即所谓的M-集）。特别地，我们证明了正则单形的最优性，描述了一些小基数的M-集，定义并讨论了球面f-设计。
英文摘要：
In the present paper, we consider the majorization theorem (also known as Karamata's inequality) and the respective minima of the majorization (the so-called M-sets) for f-energy potentials of $m$-point configurations on the unit sphere. In particular, we show the optimality of regular simplexes, describe some M-sets of small cardinality, define and discuss spherical f-designs.
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