  It is shown that for each finite number of Dirac measures supported at points
$s_n$ in three-dimensional Euclidean space, with given amplitudes $a_n$, there
exists a unique real-valued Lipschitz function $u$, vanishing at infinity,
which distributionally solves the quasi-linear elliptic partial differential
equation of divergence form
$-\nabla\cdot(\nabla{u}/\sqrt{1-|\nabla{u}|^2})=4\pi\sum_{n=1}^N a_n
\delta_{s_n}$. Moreover, $u$ is real analytic away from the $s_n$. The result
can be interpreted in at least two ways: (a) for any number of point charges of
arbitrary magnitude and sign at prescribed locations $s_n$ in three-dimensional
Euclidean space there exists a unique electrostatic field which satisfies the
Maxwell-Born-Infeld field equations smoothly away from the point charges and
vanishes as $|s|\to\infty$; (b) for any number of integral mean curvatures
assigned to locations $s_n$ there exists a unique asymptotically flat, almost
everywhere space-like maximal slice with point defects of Minkowski spacetime,
having lightcone singularities over the $s_n$ but being smooth otherwise, and
whose height function vanishes as $|s|\to\infty$. No struts between the point
singularities ever occur.
