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Suppose maximises
over all possible sets of size .
Is it true that
where the maximum is taken over all spherical caps and is the area of (normalised so that the entire sphere has area )?
Source: erdosproblems.com/991
An accepted solution exists. The statement is true.
Proved. The site labels the problem proved (page last edited
2025-09-16) on the strength of two refereed papers, while remarking that the
attribution is unclear: Brauchart (Math. Comp. 2008) proves the quantitative
bound and
regards the equidistribution itself as classical potential theory; Marzo and
Mas (Constr. Approx. 2021) prove as the case , of a
bound for Riesz energy minimizers, a rate they credit to an unpublished
manuscript of Wolff from around 1992. Each rate answers the question, so the
standing is solved/proved, derived from the two accepted claim pages
Brauchart 2008 and
Marzo and Mas 2021;
the acceptance evidence on each is the refereed publication and the site's
acceptance, not a review by this corpus.