3 problems

Ionization conjecture. The number of electrons that can be bound to an atomic nucleus of charge $Z$ cannot exceed $Z+1$; mathematically, if $N\leq Z+1$, then $I_Z^{TFDW}$ has a min…

Assume the hypotheses of the one-force-one-solution conjecture, and work almost surely. A one-sided minimiser is a curve defined on $(-\infty,t]$ such that compact perturbations fi…

Let $(x_1^n,\ldots,x_n^n)$ be a sequence of minimizing configurations, and let the additional decay hypothesis imposed in the paper be denoted by the relevant hypothesis on the fie…