5 problems

Let $e_{\rm UEG}$ denote the energy per unit volume of the three-dimensional uniform electron gas at unit density, and let $\zeta_{\rm BCC}(1)$ be the Epstein zeta value at $1$ for…

For a density $\rho$ on $\mathbb{R}^3$, let $E_{\rm ind}[\rho]$ be its indirect energy, and define the best Lieb–Oxford constant as the smallest constant $C$ such that … for all ad…

Let $c_{\rm LO}(1,3)$ be the optimal Lieb–Oxford constant for the Coulomb interaction in dimension $d=3$, and let $c_{\rm UEG}(1,3)$ denote the corresponding classical Uniform Elec…

In dimension $3$ and for the Coulomb interaction $s=1$, let $\mathsf C_{\mathrm{UEG}}(1,3)$ denote the Uniform Electron Gas next-order constant and let $\mathsf C_{\mathrm{LO}}$ de…

Uniform electron gas conjecture. The best Lieb–Oxford constant is attained for the uniform electron gas, namely,