  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.
