  In this paper for either the sharp front Surface Quasi-Geostrophic equation
or the Muskat problem we rule out the "splash singularity" blow-up scenario; in
other words we prove that the contours evolving from either of these systems
can not intersect at a single point while the free boundary remains smooth.
Splash singularities have been shown to hold for the free boundary
incompressible Euler equation in the form of the water waves contour evolution
problem \cite{ADCPJ}. Our result confirms the numerical simulations in
\cite{CFMR} where it is shown that the curvature blows up due to the contours
collapsing at a point. Here we prove that maintaining control of the curvature
will remove the possibility of pointwise interphase collapse. Another
conclusion that we provide is a better understanding of the work \cite{DP3} in
which squirt singularities are ruled out; here a positive volume of fluid
between the contours can not be ejected in finite time.
