10 problems

Conway–Guy conjecture. There is no monostable tetrahedron, but there is a monostable convex polyhedron in $\mathbb R^3$.

Let $S$ and $U$ denote, respectively, the numbers of stable and unstable equilibria of a homogeneous convex body. For a general $C^1$-smooth convex body, Arnold's conjecture. The v…

Let a finite configuration of positive charges be given, and let $\alpha>0$. Consider its nondegenerate equilibrium points and its effective Voronoi cells. Effective Voronoi-cell b…

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…

Várkonyi's conjecture. The complexity satisfies

Nasonov–Panina–Siersma conjecture. The inequality $n_{max,K} \geq 10$ holds for every $3$-dimensional convex polytope.

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…

Let $\triangle$ be a triangle with vertices $A$, $B$, and $C$. For a point $X$ in its plane, let $Q(X)$ be the triple of normalized stationary charges for which the gradient of the…

Consider a planar potential generated by $n$ Newtonian point masses together with a quadratic confining term, and let $N(n)$ denote the maximum number of equilibria over the system…

Curvature-relaxed approximation conjecture. Theorem remains true if the condition that the principal curvatures of $\operatorname{bd}(K)$ at every equilibrium point of $K$ are stri…