2 problems

Let a ball carry an equilibrium measure in the external field considered in the cited work, and let its support be the set on which that equilibrium measure is concentrated. Shell-…

Let $\mathcal{E}$ denote the Coulomb energy, let $f^*$ be an optimizer, and let $\tau$ range over translations. For a function $f$, write $f\circ\tau^{-1}$ for its translate. Guo's…