Papers Published
Abstract:
We study an isoperimetric problem the energy of which contains the perimeter
of a set, Coulomb repulsion of the set with itself, and attraction of the set
to a background nucleus as a point charge with charge $Z$. For the variational
problem with constrained volume $V$, our main result is that the minimizer does
not exist if $V - Z$ is larger than a constant multiple of $\max(Z^{2/3}, 1)$.
The main technical ingredients of our proof are a uniform density lemma and
electrostatic screening arguments.