  We investigate the evolution of the random interfaces in a two dimensional
Potts model at zero temperature under Glauber dynamics for some particular
initial conditions. We prove that under space-time diffusive scaling the shape
of the interfaces converges in probability to the solution of a non-linear
parabolic equation. This Law of Large Numbers is obtained from the Hydrodynamic
limit of a coupling between an exclusion process and an inhomogeneous one
dimensional zero range process with asymmetry at the origin.
