3 problems

Let $e_0(m)$ be the limiting energy for mass $m>0$, and let $m^\ast$ denote the threshold below which a single-ball minimizer exists. A configuration is a minimizer associated with…

Consider the limiting three-dimensional energy in which particles have masses $m^1,\ldots,m^n$ that play the role of electrical charges. Equal-mass conjecture. In three dimensions,…

Let $e_0^{\rm 3d}$ be the three-dimensional local minimization problem, and consider its global minimizers when they exist. Ball conjecture. All global minimizers of the problem…