  In this article we investigate spectral properties of the coupling
$H+V_\lambda$, where $H=-i\alpha\cdot\nabla +m\beta$ is the free Dirac operator
in $\mathbb R^3$, $m>0$ and $V_\lambda$ is an electrostatic shell potential
(which depends on a parameter $\lambda\in\mathbb R$) located on the boundary of
a smooth domain in $\mathbb R^3$. Our main result is an isoperimetric-type
inequality for the admissible range of $\lambda$'s for which the coupling
$H+V_\lambda$ generates pure point spectrum in $(-m,m)$. That the ball is the
unique optimizer of this inequality is also shown. Regarding some ingredients
of the proof, we make use of the Birman-Schwinger principle adapted to our
setting in order to prove some monotonicity property of the admissible
$\lambda$'s, and we use this to relate the endpoints of the admissible range of
$\lambda$'s to the sharp constant of a quadratic form inequality, from which
the isoperimetric-type inequality is derived.
