  For surfaces of revolution $B$ in $\R^3$, we investigate the limit
distribution of minimum energy point masses on $B$ that interact according to
the logarithmic potential $\log (1/r)$, where $r$ is the Euclidean distance
between points. We show that such limit distributions are supported only on the
``out-most'' portion of the surface (e.g., for a torus, only on that portion of
the surface with positive curvature). Our analysis proceeds by reducing the
problem to the complex plane where a non-singular potential kernel arises whose
level lines are ellipses.
