3 problems

Let $\mathbb{M}^3$ be a $3$-dimensional normed space whose unit ball has a $C^2$-class differentiable boundary and strictly positive Gaussian curvature. Existence conjecture. There…

Let $N$ positive electric charges be fixed in $\mathbb{R}^d$. Finiteness conjecture. The configuration has only finitely many points of equilibrium. The source calls this a folklor…

Consider a configuration of $N$ fixed electric charges in $\mathbb{R}^3$ having finitely many points of equilibrium. Maxwell's conjecture. The number of equilibrium points is at mo…