  In fluid dynamics, an interface splash singularity occurs when a locally
smooth interface self-intersects in finite time. By means of elementary
arguments, we prove that such a singularity cannot occur in finite time for
vortex sheet evolution, i.e. for the two-phase incompressible Euler equations.
We prove this by contradiction; we assume that a splash singularity does indeed
occur in finite time. Based on this assumption, we find precise blow-up rates
for the components of the velocity gradient which, in turn, allow us to
characterize the geometry of the evolving interface just prior to
self-intersection. The constraints on the geometry then lead to an impossible
outcome, showing that our assumption of a finite-time splash singularity was
false.
