  We consider the regularity of an interface between two incompressible and
inviscid fluids flows in the presence of surface tension. We obtain local in
time estimates on the interface in $H^{\frac32k +1}$ and the velocity fields in
$H^{\frac32k}$. These estimates are obtained using geometric considerations
which show that the Kelvin-Helmholtz instabilities are a consequence of a
curvature calculation.
