Maximum number of electrostatic equilibria

Determine the maximum possible number of equilibria of an electrostatic potential generated by n point charges in R^3.

Background

The central problem of the paper is to understand how many equilibria can be generated by an electrostatic potential associated with finitely many point charges. The authors provide constructions with asymptotically more than three equilibria per charge, but no matching upper bound or exact extremal value.

The unresolved extremal problem is broader than the specific 25n/7 threshold question and includes determining the true growth rate and optimal configurations.

References

The main question of determining the maximum number of equilibria of an electrostatic potential defined by $n$ point charges in $R3$ remains open.

— Counting Equilibria of the Electrostatic Potential  (2501.05315 - Edelsbrunner et al., 9 Jan 2025) in Discussion, Section 7