Thinking outside the box: the uniform electron gas on a hypersphere

We discuss alternative homogeneous electron gas systems in which a finite number $n$ of electrons are confined to a $D$-dimensional sphere. We derive the first few terms of the high-density ($r_s\to0$, where $r_s$ is the Seitz radius) energy expansions for these systems and show that, in the thermodynamic limit ($n\to\infty$), these terms become identical to those of $D$-dimensional jellium.